diff --git a/.babelrc b/.babelrc
index 332bba6f9..4b5a10170 100644
--- a/.babelrc
+++ b/.babelrc
@@ -5,6 +5,9 @@
                 ["@babel/preset-env", {
                     "modules": false
                 }]
+            ],
+            "plugins": [
+                "./babel-plugin-es-import-extensions"
             ]
         },
         "development": {
diff --git a/babel-plugin-es-import-extensions.js b/babel-plugin-es-import-extensions.js
new file mode 100644
index 000000000..ae2d91a92
--- /dev/null
+++ b/babel-plugin-es-import-extensions.js
@@ -0,0 +1,38 @@
+/*
+ * Babel plugin used by the ES module build (`npm run build:es`, see `.babelrc`).
+ *
+ * Node.js requires relative import paths in ES modules to include the file
+ * extension, so `import assertString from './util/assertString'` is rewritten
+ * to `import assertString from './util/assertString.js'`.
+ */
+const fs = require('fs');
+const path = require('path');
+
+function isFile(file) {
+  try {
+    return fs.statSync(file).isFile();
+  } catch (err) {
+    return false;
+  }
+}
+
+module.exports = function esImportExtensions() {
+  function addExtension(nodePath, state) {
+    const { source } = nodePath.node;
+    if (!source || !/^\.\.?\//.test(source.value)) return;
+    const file = path.resolve(path.dirname(state.filename), source.value);
+    if (isFile(file)) return;
+    if (!isFile(`${file}.js`)) {
+      throw nodePath.buildCodeFrameError(`Cannot resolve "${source.value}" to a file`);
+    }
+    source.value = `${source.value}.js`;
+  }
+
+  return {
+    visitor: {
+      ImportDeclaration: addExtension,
+      ExportNamedDeclaration: addExtension,
+      ExportAllDeclaration: addExtension,
+    },
+  };
+};
diff --git a/test/esBuild.test.js b/test/esBuild.test.js
new file mode 100644
index 000000000..e043fb767
--- /dev/null
+++ b/test/esBuild.test.js
@@ -0,0 +1,37 @@
+import assert from 'assert';
+import fs from 'fs';
+import path from 'path';
+
+const esDir = path.join(__dirname, '..', 'es');
+
+function listFiles(dir) {
+  return fs.readdirSync(dir).reduce((files, name) => {
+    const file = path.join(dir, name);
+    return files.concat(fs.statSync(file).isDirectory() ? listFiles(file) : [file]);
+  }, []);
+}
+
+describe('ES module build', () => {
+  it('should use the file extension in relative import paths', () => {
+    const files = listFiles(esDir).filter(file => path.extname(file) === '.js');
+    let checked = 0;
+    files.forEach((file) => {
+      const code = fs.readFileSync(file, 'utf8');
+      const importRegex = /^(?:import|export)\s[^;]*?\sfrom\s+['"]([^'"]+)['"]/gm;
+      let match = importRegex.exec(code);
+      while (match) {
+        const specifier = match[1];
+        if (specifier[0] === '.') {
+          checked += 1;
+          const target = path.resolve(path.dirname(file), specifier);
+          assert.ok(
+            path.extname(specifier) === '.js' && fs.existsSync(target) && fs.statSync(target).isFile(),
+            `${path.relative(esDir, file)} imports "${specifier}", which is not a path to a file`
+          );
+        }
+        match = importRegex.exec(code);
+      }
+    });
+    assert.ok(checked > 0, 'No relative imports found in the ES module build. Run `npm run build:es`');
+  });
+});