diff --git a/pkg/analysis_server/lib/src/services/correction/dart/flutter_wrap.dart b/pkg/analysis_server/lib/src/services/correction/dart/flutter_wrap.dart
index 0c077db5ff2..f03127c8739 100644
--- a/pkg/analysis_server/lib/src/services/correction/dart/flutter_wrap.dart
+++ b/pkg/analysis_server/lib/src/services/correction/dart/flutter_wrap.dart
@@ -46,7 +46,19 @@ class FlutterWrap extends MultiCorrectionProducer {
         widgetExpressions.add(selectedNode);
       }
     } else {
-      var widget = flutter.identifyWidgetExpression(analyzer.coveringNode);
+      var coveringNode = analyzer.coveringNode;
+
+      // If the coveringNode is an argument list but the caret is exactly at the
+      // start (before the opening paren) we should use the parent instead
+      // as the user associates this location with the widget name:
+      //
+      //     Text^('foo')
+      if (coveringNode is ArgumentList &&
+          coveringNode.offset == selectionOffset) {
+        coveringNode = coveringNode.parent;
+      }
+
+      var widget = flutter.identifyWidgetExpression(coveringNode);
       if (widget != null) {
         widgetExpressions.add(widget);
       }
diff --git a/pkg/analysis_server/test/src/services/correction/assist/flutter_wrap_column_test.dart b/pkg/analysis_server/test/src/services/correction/assist/flutter_wrap_column_test.dart
index ce2a3ba2541..c16385a6550 100644
--- a/pkg/analysis_server/test/src/services/correction/assist/flutter_wrap_column_test.dart
+++ b/pkg/analysis_server/test/src/services/correction/assist/flutter_wrap_column_test.dart
@@ -118,6 +118,36 @@ class FakeFlutter {
     ]);
   }
 }
+''');
+  }
+
+  Future<void> test_endOfWidgetName() async {
+    addFlutterPackage();
+    await resolveTestUnit('''
+import 'package:flutter/widgets.dart';
+
+class FakeFlutter {
+  main() {
+    return Container(
+      child: Text/*caret*/('aaa'),
+    );
+  }
+}
+''');
+    await assertHasAssist('''
+import 'package:flutter/widgets.dart';
+
+class FakeFlutter {
+  main() {
+    return Container(
+      child: Column(
+        children: [
+          Text('aaa'),
+        ],
+      ),
+    );
+  }
+}
 ''');
   }
 }