diff --git a/packages/next/build/webpack/config/blocks/css/index.ts b/packages/next/build/webpack/config/blocks/css/index.ts
index b807fe24926fe..bd99853ee2534 100644
--- a/packages/next/build/webpack/config/blocks/css/index.ts
+++ b/packages/next/build/webpack/config/blocks/css/index.ts
@@ -104,6 +104,7 @@ export const css = curry(async function css(
               options: {
                 importLoaders: 1,
                 sourceMap: true,
+                onlyLocals: ctx.isServer,
                 modules: {
                   // Disallow global style exports so we can code-split CSS and
                   // not worry about loading order.
diff --git a/test/integration/css/fixtures/single-module/pages/index.js b/test/integration/css/fixtures/single-module/pages/index.js
new file mode 100644
index 0000000000000..79140b6b136c9
--- /dev/null
+++ b/test/integration/css/fixtures/single-module/pages/index.js
@@ -0,0 +1,11 @@
+import { redText } from './index.module.css'
+
+function Home() {
+  return (
+    <div id="verify-red" className={redText}>
+      This text should be red.
+    </div>
+  )
+}
+
+export default Home
diff --git a/test/integration/css/fixtures/single-module/pages/index.module.css b/test/integration/css/fixtures/single-module/pages/index.module.css
new file mode 100644
index 0000000000000..08a38e09ef8ea
--- /dev/null
+++ b/test/integration/css/fixtures/single-module/pages/index.module.css
@@ -0,0 +1,3 @@
+.redText {
+  color: red;
+}
diff --git a/test/integration/css/test/index.test.js b/test/integration/css/test/index.test.js
index fe94594d59275..3a817c135d481 100644
--- a/test/integration/css/test/index.test.js
+++ b/test/integration/css/test/index.test.js
@@ -203,19 +203,19 @@ describe('CSS Support', () => {
 
       const { version, mappings, sourcesContent } = JSON.parse(cssMapContent)
       expect({ version, mappings, sourcesContent }).toMatchInlineSnapshot(`
-        Object {
-          "mappings": "AAAA,+CACE,4BACE,WACF,CAFA,mBACE,WACF,CAFA,uBACE,WACF,CAFA,wBACE,WACF,CAFA,cACE,WACF,CACF",
-          "sourcesContent": Array [
-            "@media (480px <= width < 768px) {
-          ::placeholder {
-            color: green;
-          }
-        }
-        ",
-          ],
-          "version": 3,
-        }
-      `)
+                        Object {
+                          "mappings": "AAAA,+CACE,4BACE,WACF,CAFA,mBACE,WACF,CAFA,uBACE,WACF,CAFA,wBACE,WACF,CAFA,cACE,WACF,CACF",
+                          "sourcesContent": Array [
+                            "@media (480px <= width < 768px) {
+                          ::placeholder {
+                            color: green;
+                          }
+                        }
+                        ",
+                          ],
+                          "version": 3,
+                        }
+                  `)
     })
   })
 
@@ -261,25 +261,25 @@ describe('CSS Support', () => {
 
       const { version, mappings, sourcesContent } = JSON.parse(cssMapContent)
       expect({ version, mappings, sourcesContent }).toMatchInlineSnapshot(`
-        Object {
-          "mappings": "AACA,gCACE,cACE,WACF,CACF,CAGA,OACE,eAA0B,CAA1B,gBACF",
-          "sourcesContent": Array [
-            "/* this should pass through untransformed */
-        @media (480px <= width < 768px) {
-          ::placeholder {
-            color: green;
-          }
-        }
-
-        /* this should be transformed to width/height */
-        .video {
-          -xyz-max-size: 400px 300px;
-        }
-        ",
-          ],
-          "version": 3,
-        }
-      `)
+                        Object {
+                          "mappings": "AACA,gCACE,cACE,WACF,CACF,CAGA,OACE,eAA0B,CAA1B,gBACF",
+                          "sourcesContent": Array [
+                            "/* this should pass through untransformed */
+                        @media (480px <= width < 768px) {
+                          ::placeholder {
+                            color: green;
+                          }
+                        }
+
+                        /* this should be transformed to width/height */
+                        .video {
+                          -xyz-max-size: 400px 300px;
+                        }
+                        ",
+                          ],
+                          "version": 3,
+                        }
+                  `)
     })
   })
 
@@ -674,12 +674,12 @@ describe('CSS Support', () => {
           )
           .sort()
       ).toMatchInlineSnapshot(`
-        Array [
-          "dark.svg",
-          "dark2.svg",
-          "light.svg",
-        ]
-      `)
+                        Array [
+                          "dark.svg",
+                          "dark2.svg",
+                          "light.svg",
+                        ]
+                  `)
     })
   })
 
@@ -800,4 +800,60 @@ describe('CSS Support', () => {
       expect(cssMapFiles.length).toBe(1)
     })
   })
+
+  describe('Basic CSS Module Support', () => {
+    const appDir = join(fixturesDir, 'single-module')
+
+    beforeAll(async () => {
+      await remove(join(appDir, '.next'))
+    })
+
+    let appPort
+    let app
+    beforeAll(async () => {
+      await nextBuild(appDir)
+      const server = nextServer({
+        dir: appDir,
+        dev: false,
+        quiet: true,
+      })
+
+      app = await startApp(server)
+      appPort = app.address().port
+    })
+    afterAll(async () => {
+      await stopApp(app)
+    })
+
+    it(`should've emitted a single CSS file`, async () => {
+      const cssFolder = join(appDir, '.next/static/css')
+
+      const files = await readdir(cssFolder)
+      const cssFiles = files.filter(f => /\.css$/.test(f))
+
+      expect(cssFiles.length).toBe(1)
+      const cssContent = await readFile(join(cssFolder, cssFiles[0]), 'utf8')
+
+      expect(
+        cssContent.replace(/\/\*.*?\*\//g, '').trim()
+      ).toMatchInlineSnapshot(`".index_redText__3CwEB{color:red}"`)
+    })
+
+    it(`should've injected the CSS on server render`, async () => {
+      const content = await renderViaHTTP(appPort, '/')
+      const $ = cheerio.load(content)
+
+      const cssPreload = $('link[rel="preload"][as="style"]')
+      expect(cssPreload.length).toBe(1)
+      expect(cssPreload.attr('href')).toMatch(/^\/_next\/static\/css\/.*\.css$/)
+
+      const cssSheet = $('link[rel="stylesheet"]')
+      expect(cssSheet.length).toBe(1)
+      expect(cssSheet.attr('href')).toMatch(/^\/_next\/static\/css\/.*\.css$/)
+
+      expect($('#verify-red').attr('class')).toMatchInlineSnapshot(
+        `"index_redText__3CwEB"`
+      )
+    })
+  })
 })