diff --git a/packages/flutter/lib/src/material/date_picker.dart b/packages/flutter/lib/src/material/date_picker.dart
index bc28ca39796..4eace111935 100644
--- a/packages/flutter/lib/src/material/date_picker.dart
+++ b/packages/flutter/lib/src/material/date_picker.dart
@@ -777,13 +777,21 @@ class _DatePickerDialogState extends State<DatePickerDialog> with RestorationMix
 
               switch (orientation) {
                 case Orientation.portrait:
+                  final bool isInputMode =
+                      _entryMode.value == DatePickerEntryMode.inputOnly ||
+                      _entryMode.value == DatePickerEntryMode.input;
+                  // When the portrait dialog does not fit vertically, hide the header when the entry mode
+                  // is input, or hide the picker when the entry mode is not input.
+                  final bool showHeader = isFullyPortrait || !isInputMode;
+                  final bool showPicker = isFullyPortrait || isInputMode;
+
                   return Column(
                     mainAxisSize: MainAxisSize.min,
                     crossAxisAlignment: CrossAxisAlignment.stretch,
                     children: <Widget>[
-                      header,
+                      if (showHeader) header,
                       if (useMaterial3) Divider(height: 0, color: datePickerTheme.dividerColor),
-                      if (isFullyPortrait) ...<Widget>[Expanded(child: picker), actions],
+                      if (showPicker) ...<Widget>[Expanded(child: picker), actions],
                     ],
                   );
                 case Orientation.landscape:
@@ -3175,10 +3183,8 @@ class _InputDateRangePickerDialog extends StatelessWidget {
             return Column(
               mainAxisSize: MainAxisSize.min,
               crossAxisAlignment: CrossAxisAlignment.stretch,
-              children: <Widget>[
-                header,
-                if (isFullyPortrait) ...<Widget>[Expanded(child: picker), actions],
-              ],
+              // When the portrait dialog does not fit vertically, hide the header.
+              children: <Widget>[if (isFullyPortrait) header, Expanded(child: picker), actions],
             );
           },
         );
diff --git a/packages/flutter/test/material/date_picker_test.dart b/packages/flutter/test/material/date_picker_test.dart
index f500a132ea5..f712364b53b 100644
--- a/packages/flutter/test/material/date_picker_test.dart
+++ b/packages/flutter/test/material/date_picker_test.dart
@@ -1662,6 +1662,31 @@ void main() {
       });
     });
 
+    // Regression test for https://github.com/flutter/flutter/issues/140311.
+    testWidgets('Text field stays visible when orientation is portrait and height is reduced', (
+      WidgetTester tester,
+    ) async {
+      addTearDown(tester.view.reset);
+      tester.view.physicalSize = const Size(720, 1280);
+      tester.view.devicePixelRatio = 1.0;
+      initialEntryMode = DatePickerEntryMode.input;
+
+      // Text field and header are visible by default.
+      await prepareDatePicker(tester, useMaterial3: true, (Future<DateTime?> range) async {
+        expect(find.byType(TextField), findsOneWidget);
+        expect(find.text('Select date'), findsOne);
+      });
+
+      // Simulate the portait mode on a device with a small display when the virtual
+      // keyboard is visible.
+      tester.view.viewInsets = const FakeViewPadding(bottom: 1000);
+      await tester.pumpAndSettle();
+
+      // Text field is visible and header is hidden.
+      expect(find.byType(TextField), findsOneWidget);
+      expect(find.text('Select date'), findsNothing);
+    });
+
     // This is a regression test for https://github.com/flutter/flutter/issues/139120.
     testWidgets('Dialog contents are visible - textScaler 0.88, 1.0, 2.0', (
       WidgetTester tester,
diff --git a/packages/flutter/test/material/date_range_picker_test.dart b/packages/flutter/test/material/date_range_picker_test.dart
index 46139146144..92371173479 100644
--- a/packages/flutter/test/material/date_range_picker_test.dart
+++ b/packages/flutter/test/material/date_range_picker_test.dart
@@ -1243,6 +1243,31 @@ void main() {
         expect(tester.takeException(), null);
       });
     });
+
+    // Regression test for https://github.com/flutter/flutter/issues/140311.
+    testWidgets('Text field stays visible when orientation is portrait and height is reduced', (
+      WidgetTester tester,
+    ) async {
+      addTearDown(tester.view.reset);
+      tester.view.physicalSize = const Size(720, 1280);
+      tester.view.devicePixelRatio = 1.0;
+      initialEntryMode = DatePickerEntryMode.input;
+
+      // Text fields and header are visible by default.
+      await preparePicker(tester, useMaterial3: true, (Future<DateTimeRange?> range) async {
+        expect(find.byType(TextField), findsNWidgets(2));
+        expect(find.text('Select range'), findsOne);
+      });
+
+      // Simulate the portait mode on a device with a small display when the virtual
+      // keyboard is visible.
+      tester.view.viewInsets = const FakeViewPadding(bottom: 1000);
+      await tester.pumpAndSettle();
+
+      // Text fields are visible and header is hidden
+      expect(find.byType(TextField), findsNWidgets(2));
+      expect(find.text('Select range'), findsNothing);
+    });
   });
 
   testWidgets('DatePickerDialog is state restorable', (WidgetTester tester) async {