diff --git a/packages/flutter/lib/src/material/data_table.dart b/packages/flutter/lib/src/material/data_table.dart
index 4d9c29f06c5..3f87bfcd402 100644
--- a/packages/flutter/lib/src/material/data_table.dart
+++ b/packages/flutter/lib/src/material/data_table.dart
@@ -330,6 +330,7 @@ class DataTable extends StatelessWidget {
     this.headingRowHeight = 56.0,
     this.horizontalMargin = 24.0,
     this.columnSpacing = 56.0,
+    this.showCheckboxColumn = true,
     @required this.rows,
   }) : assert(columns != null),
        assert(columns.isNotEmpty),
@@ -339,6 +340,7 @@ class DataTable extends StatelessWidget {
        assert(headingRowHeight != null),
        assert(horizontalMargin != null),
        assert(columnSpacing != null),
+       assert(showCheckboxColumn != null),
        assert(rows != null),
        assert(!rows.any((DataRow row) => row.cells.length != columns.length)),
        _onlyTextColumn = _initOnlyTextColumn(columns),
@@ -408,6 +410,17 @@ class DataTable extends StatelessWidget {
   /// This value defaults to 56.0 to adhere to the Material Design specifications.
   final double columnSpacing;
 
+  /// {@template flutter.material.dataTable.showCheckboxColumn}
+  /// Whether the widget should display checkboxes for selectable rows.
+  ///
+  /// If true, a [CheckBox] will be placed at the beginning of each row that is
+  /// selectable. However, if [DataRow.onSelectChanged] is not set for any row,
+  /// checkboxes will not be placed, even if this value is true.
+  ///
+  /// If false, all rows will not display a [CheckBox].
+  /// {@endtemplate}
+  final bool showCheckboxColumn;
+
   /// The data to show in each row (excluding the row that contains
   /// the column headings).
   ///
@@ -608,10 +621,10 @@ class DataTable extends StatelessWidget {
       border: Border(bottom: Divider.createBorderSide(context, width: 1.0)),
     );
 
-    final bool showCheckboxColumn = rows.any((DataRow row) => row.onSelectChanged != null);
-    final bool allChecked = showCheckboxColumn && !rows.any((DataRow row) => row.onSelectChanged != null && !row.selected);
+    final bool displayCheckboxColumn = showCheckboxColumn && rows.any((DataRow row) => row.onSelectChanged != null);
+    final bool allChecked = displayCheckboxColumn && !rows.any((DataRow row) => row.onSelectChanged != null && !row.selected);
 
-    final List<TableColumnWidth> tableColumns = List<TableColumnWidth>(columns.length + (showCheckboxColumn ? 1 : 0));
+    final List<TableColumnWidth> tableColumns = List<TableColumnWidth>(columns.length + (displayCheckboxColumn ? 1 : 0));
     final List<TableRow> tableRows = List<TableRow>.generate(
       rows.length + 1, // the +1 is for the header row
       (int index) {
@@ -627,7 +640,7 @@ class DataTable extends StatelessWidget {
     int rowIndex;
 
     int displayColumnIndex = 0;
-    if (showCheckboxColumn) {
+    if (displayCheckboxColumn) {
       tableColumns[0] = FixedColumnWidth(horizontalMargin + Checkbox.width + horizontalMargin / 2.0);
       tableRows[0].children[0] = _buildCheckbox(
         color: theme.accentColor,
@@ -651,9 +664,9 @@ class DataTable extends StatelessWidget {
       final DataColumn column = columns[dataColumnIndex];
 
       double paddingStart;
-      if (dataColumnIndex == 0 && showCheckboxColumn) {
+      if (dataColumnIndex == 0 && displayCheckboxColumn) {
         paddingStart = horizontalMargin / 2.0;
-      } else if (dataColumnIndex == 0 && !showCheckboxColumn) {
+      } else if (dataColumnIndex == 0 && !displayCheckboxColumn) {
         paddingStart = horizontalMargin;
       } else {
         paddingStart = columnSpacing / 2.0;
diff --git a/packages/flutter/lib/src/material/paginated_data_table.dart b/packages/flutter/lib/src/material/paginated_data_table.dart
index 50147a48a04..4f634d86188 100644
--- a/packages/flutter/lib/src/material/paginated_data_table.dart
+++ b/packages/flutter/lib/src/material/paginated_data_table.dart
@@ -74,6 +74,7 @@ class PaginatedDataTable extends StatefulWidget {
     this.headingRowHeight = 56.0,
     this.horizontalMargin = 24.0,
     this.columnSpacing = 56.0,
+    this.showCheckboxColumn = true,
     this.initialFirstRowIndex = 0,
     this.onPageChanged,
     this.rowsPerPage = defaultRowsPerPage,
@@ -91,6 +92,7 @@ class PaginatedDataTable extends StatefulWidget {
        assert(headingRowHeight != null),
        assert(horizontalMargin != null),
        assert(columnSpacing != null),
+       assert(showCheckboxColumn != null),
        assert(rowsPerPage != null),
        assert(rowsPerPage > 0),
        assert(() {
@@ -164,6 +166,9 @@ class PaginatedDataTable extends StatefulWidget {
   /// This value defaults to 56.0 to adhere to the Material Design specifications.
   final double columnSpacing;
 
+  /// {@macro flutter.material.dataTable.showCheckboxColumn}
+  final bool showCheckboxColumn;
+
   /// The index of the first row to display when the widget is first created.
   final int initialFirstRowIndex;
 
@@ -465,6 +470,7 @@ class PaginatedDataTableState extends State<PaginatedDataTable> {
               headingRowHeight: widget.headingRowHeight,
               horizontalMargin: widget.horizontalMargin,
               columnSpacing: widget.columnSpacing,
+              showCheckboxColumn: widget.showCheckboxColumn,
               rows: _getRows(_firstRowIndex, widget.rowsPerPage),
             ),
           ),
diff --git a/packages/flutter/test/material/data_table_test.dart b/packages/flutter/test/material/data_table_test.dart
index 4a9d5597722..4763962f3c5 100644
--- a/packages/flutter/test/material/data_table_test.dart
+++ b/packages/flutter/test/material/data_table_test.dart
@@ -99,6 +99,72 @@ void main() {
     log.clear();
   });
 
+  testWidgets('DataTable control test - no checkboxes', (WidgetTester tester) async {
+    final List<String> log = <String>[];
+
+    Widget buildTable({ bool checkboxes = false }) {
+      return DataTable(
+        showCheckboxColumn: checkboxes,
+        onSelectAll: (bool value) {
+          log.add('select-all: $value');
+        },
+        columns: const <DataColumn>[
+          DataColumn(
+            label: Text('Name'),
+            tooltip: 'Name',
+          ),
+          DataColumn(
+            label: Text('Calories'),
+            tooltip: 'Calories',
+            numeric: true,
+          ),
+        ],
+        rows: kDesserts.map<DataRow>((Dessert dessert) {
+          return DataRow(
+            key: ValueKey<String>(dessert.name),
+            onSelectChanged: (bool selected) {
+              log.add('row-selected: ${dessert.name}');
+            },
+            cells: <DataCell>[
+              DataCell(
+                Text(dessert.name),
+              ),
+              DataCell(
+                Text('${dessert.calories}'),
+                showEditIcon: true,
+                onTap: () {
+                  log.add('cell-tap: ${dessert.calories}');
+                },
+              ),
+            ],
+          );
+        }).toList(),
+      );
+    }
+
+    await tester.pumpWidget(MaterialApp(
+      home: Material(child: buildTable()),
+    ));
+
+    expect(find.byType(Checkbox), findsNothing);
+    await tester.tap(find.text('Cupcake'));
+
+    expect(log, <String>['row-selected: Cupcake']);
+    log.clear();
+
+    await tester.pumpWidget(MaterialApp(
+      home: Material(child: buildTable(checkboxes: true)),
+    ));
+
+    await tester.pumpAndSettle(const Duration(milliseconds: 200));
+    final Finder checkboxes = find.byType(Checkbox);
+    expect(checkboxes, findsNWidgets(11));
+    await tester.tap(checkboxes.first);
+
+    expect(log, <String>['select-all: true']);
+    log.clear();
+  });
+
   testWidgets('DataTable overflow test - header', (WidgetTester tester) async {
     await tester.pumpWidget(
       MaterialApp(