diff --git a/packages/react-scripts/config/webpack.config.prod.js b/packages/react-scripts/config/webpack.config.prod.js
index 87b61980eac..8fe4f6189c6 100644
--- a/packages/react-scripts/config/webpack.config.prod.js
+++ b/packages/react-scripts/config/webpack.config.prod.js
@@ -158,7 +158,17 @@ module.exports = {
         sourceMap: shouldUseSourceMap,
       }),
       new OptimizeCSSAssetsPlugin({
-        cssProcessorOptions: { parser: safePostCssParser },
+        cssProcessorOptions: {
+          parser: safePostCssParser,
+          map: {
+            // `inline: false` forces the sourcemap to be output into a
+            // separate file
+            inline: false,
+            // `annotation: true` appends the sourceMappingURL to the end of
+            // the css file, helping the browser find the sourcemap
+            annotation: true,
+          },
+        },
       }),
     ],
     // Automatically split vendor and commons