diff --git a/packages/flutter/lib/src/material/time_picker.dart b/packages/flutter/lib/src/material/time_picker.dart
index 24ab9c9931..4ae5d13cd4 100644
--- a/packages/flutter/lib/src/material/time_picker.dart
+++ b/packages/flutter/lib/src/material/time_picker.dart
@@ -247,6 +247,8 @@ class _DayPeriodControl extends StatelessWidget {
     );
     final bool layoutPortrait = orientation == Orientation.portrait;
 
+    final double buttonTextScaleFactor = math.min(MediaQuery.of(context).textScaleFactor, 2.0);
+
     final Widget amButton = ConstrainedBox(
       constraints: _kMinTappableRegion,
       child: Material(
@@ -261,7 +263,11 @@ class _DayPeriodControl extends StatelessWidget {
               heightFactor: 1,
               child: Semantics(
                 selected: amSelected,
-                child: Text(materialLocalizations.anteMeridiemAbbreviation, style: amStyle),
+                child: Text(
+                    materialLocalizations.anteMeridiemAbbreviation,
+                    style: amStyle,
+                    textScaleFactor: buttonTextScaleFactor,
+                ),
               ),
             ),
           ),
@@ -284,7 +290,11 @@ class _DayPeriodControl extends StatelessWidget {
               heightFactor: 1,
               child: Semantics(
                 selected: !amSelected,
-                child: Text(materialLocalizations.postMeridiemAbbreviation, style: pmStyle),
+                child: Text(
+                    materialLocalizations.postMeridiemAbbreviation,
+                    style: pmStyle,
+                    textScaleFactor: buttonTextScaleFactor,
+                ),
               ),
             ),
           ),
@@ -383,7 +393,12 @@ class _HourControl extends StatelessWidget {
           type: MaterialType.transparency,
           child: InkWell(
             onTap: Feedback.wrapForTap(() => fragmentContext.onModeChange(_TimePickerMode.hour), context),
-            child: Text(formattedHour, style: hourStyle, textAlign: TextAlign.end),
+            child: Text(
+              formattedHour,
+              style: hourStyle,
+              textAlign: TextAlign.end,
+              textScaleFactor: 1.0,
+            ),
           ),
         ),
       ),
@@ -404,7 +419,7 @@ class _StringFragment extends StatelessWidget {
   @override
   Widget build(BuildContext context) {
     return ExcludeSemantics(
-      child: Text(value, style: fragmentContext.inactiveStyle),
+      child: Text(value, style: fragmentContext.inactiveStyle, textScaleFactor: 1.0),
     );
   }
 }
@@ -453,7 +468,7 @@ class _MinuteControl extends StatelessWidget {
           type: MaterialType.transparency,
           child: InkWell(
             onTap: Feedback.wrapForTap(() => fragmentContext.onModeChange(_TimePickerMode.minute), context),
-            child: Text(formattedMinute, style: minuteStyle, textAlign: TextAlign.start),
+            child: Text(formattedMinute, style: minuteStyle, textAlign: TextAlign.start, textScaleFactor: 1.0),
           ),
         ),
       ),
@@ -1326,13 +1341,13 @@ class _DialState extends State<_Dial> with SingleTickerProviderStateMixin {
 
   _TappableLabel _buildTappableLabel(TextTheme textTheme, int value, String label, VoidCallback onTap) {
     final TextStyle style = textTheme.subhead;
-    // TODO(abarth): Handle textScaleFactor.
-    // https://github.com/flutter/flutter/issues/5939
+    final double labelScaleFactor = math.min(MediaQuery.of(context).textScaleFactor, 2.0);
     return _TappableLabel(
       value: value,
       painter: TextPainter(
         text: TextSpan(style: style, text: label),
         textDirection: TextDirection.ltr,
+        textScaleFactor: labelScaleFactor,
       )..layout(),
       onTap: onTap,
     );
diff --git a/packages/flutter/test/material/time_picker_test.dart b/packages/flutter/test/material/time_picker_test.dart
index d5a4d439cb..629fbddf1d 100644
--- a/packages/flutter/test/material/time_picker_test.dart
+++ b/packages/flutter/test/material/time_picker_test.dart
@@ -261,6 +261,7 @@ void _tests() {
     WidgetTester tester,
     bool alwaysUse24HourFormat, {
     TimeOfDay initialTime = const TimeOfDay(hour: 7, minute: 0),
+    double textScaleFactor = 1.0,
   }) async {
     await tester.pumpWidget(
       Localizations(
@@ -270,7 +271,10 @@ void _tests() {
           DefaultWidgetsLocalizations.delegate,
         ],
         child: MediaQuery(
-          data: MediaQueryData(alwaysUse24HourFormat: alwaysUse24HourFormat),
+          data: MediaQueryData(
+            alwaysUse24HourFormat: alwaysUse24HourFormat,
+            textScaleFactor: textScaleFactor,
+          ),
           child: Material(
             child: Directionality(
               textDirection: TextDirection.ltr,
@@ -689,6 +693,53 @@ void _tests() {
     expect(rootObserver.pickerCount, 0);
     expect(nestedObserver.pickerCount, 1);
   });
+
+  testWidgets('text scale affects certain elements and not others',
+      (WidgetTester tester) async {
+    await mediaQueryBoilerplate(
+        tester,
+        false,
+        textScaleFactor: 1.0,
+        initialTime: const TimeOfDay(hour: 7, minute: 41),
+    );
+    await tester.tap(find.text('X'));
+    await tester.pumpAndSettle();
+
+    final double minutesDisplayHeight = tester.getSize(find.text('41')).height;
+    final double amHeight = tester.getSize(find.text('AM')).height;
+
+    await tester.tap(find.text('OK')); // dismiss the dialog
+    await tester.pumpAndSettle();
+
+    // Verify that the time display is not affected by text scale.
+    await mediaQueryBoilerplate(
+        tester,
+        false,
+        textScaleFactor: 2.0,
+        initialTime: const TimeOfDay(hour: 7, minute: 41),
+    );
+    await tester.tap(find.text('X'));
+    await tester.pumpAndSettle();
+
+    expect(tester.getSize(find.text('41')).height, equals(minutesDisplayHeight));
+    expect(tester.getSize(find.text('AM')).height, equals(amHeight * 2));
+
+    await tester.tap(find.text('OK')); // dismiss the dialog
+    await tester.pumpAndSettle();
+
+    // Verify that text scale for AM/PM is at most 2x.
+    await mediaQueryBoilerplate(
+        tester,
+        false,
+        textScaleFactor: 3.0,
+        initialTime: const TimeOfDay(hour: 7, minute: 41),
+    );
+    await tester.tap(find.text('X'));
+    await tester.pumpAndSettle();
+
+    expect(tester.getSize(find.text('41')).height, equals(minutesDisplayHeight));
+    expect(tester.getSize(find.text('AM')).height, equals(amHeight * 2));
+  });
 }
 
 final Finder findDialPaint = find.descendant(