diff --git a/git-submodule.sh b/git-submodule.sh
index 8b90589717..514d2eb7ab 100755
--- a/git-submodule.sh
+++ b/git-submodule.sh
@@ -464,8 +464,11 @@ cmd_update()
 
 			if test -z "$nofetch"
 			then
+				# Run fetch only if $sha1 isn't present or it
+				# is not reachable from a ref.
 				(clear_local_git_env; cd "$path" &&
-					git-fetch) ||
+					((rev=$(git rev-list -n 1 $sha1 --not --all 2>/dev/null) &&
+					 test -z "$rev") || git-fetch)) ||
 				die "Unable to fetch in submodule path '$path'"
 			fi
 
diff --git a/t/t7406-submodule-update.sh b/t/t7406-submodule-update.sh
index bfb4975e94..ee3eec5157 100755
--- a/t/t7406-submodule-update.sh
+++ b/t/t7406-submodule-update.sh
@@ -74,6 +74,26 @@ test_expect_success 'submodule update detaching the HEAD ' '
 	)
 '
 
+apos="'";
+test_expect_success 'submodule update does not fetch already present commits' '
+	(cd submodule &&
+	  echo line3 >> file &&
+	  git add file &&
+	  test_tick &&
+	  git commit -m "upstream line3"
+	) &&
+	(cd super/submodule &&
+	  head=$(git rev-parse --verify HEAD) &&
+	  echo "Submodule path ${apos}submodule$apos: checked out $apos$head$apos" > ../../expected &&
+	  git reset --hard HEAD~1
+	) &&
+	(cd super &&
+	  git submodule update > ../actual 2> ../actual.err
+	) &&
+	test_cmp expected actual &&
+	! test -s actual.err
+'
+
 test_expect_success 'submodule update --rebase staying on master' '
 	(cd super/submodule &&
 	  git checkout master