diff --git a/babel.config.cjs b/babel.config.cjs
index d5c314af15..23ab202ae0 100644
--- a/babel.config.cjs
+++ b/babel.config.cjs
@@ -31,5 +31,22 @@ module.exports = {
         "@babel/plugin-transform-object-rest-spread",
         "@babel/plugin-syntax-dynamic-import",
         "@babel/plugin-transform-runtime",
+        [
+            "search-and-replace",
+            {
+                // Since rewriteImportExtensions doesn't work on dynamic imports (yet), we need to manually replace
+                // the dynamic rust-crypto import.
+                // (see https://github.com/babel/babel/issues/16750)
+                rules:
+                    process.env.NODE_ENV !== "test"
+                        ? [
+                              {
+                                  search: "./rust-crypto/index.ts",
+                                  replace: "./rust-crypto/index.js",
+                              },
+                          ]
+                        : [],
+            },
+        ],
     ],
 };
diff --git a/package.json b/package.json
index 46687405ca..e2e274b8b2 100644
--- a/package.json
+++ b/package.json
@@ -91,6 +91,7 @@
         "@typescript-eslint/eslint-plugin": "^7.0.0",
         "@typescript-eslint/parser": "^7.0.0",
         "babel-jest": "^29.0.0",
+        "babel-plugin-search-and-replace": "^1.1.1",
         "debug": "^4.3.4",
         "eslint": "8.57.0",
         "eslint-config-google": "^0.14.0",
diff --git a/src/client.ts b/src/client.ts
index 3a9860b3a8..514586047a 100644
--- a/src/client.ts
+++ b/src/client.ts
@@ -2254,9 +2254,7 @@ export class MatrixClient extends TypedEventEmitter<EmittedEvents, ClientEventHa
         // importing rust-crypto will download the webassembly, so we delay it until we know it will be
         // needed.
         this.logger.debug("Downloading Rust crypto library");
-        // blocked on https://github.com/matrix-org/matrix-js-sdk/issues/4392 / https://github.com/babel/babel/issues/16750
-        // eslint-disable-next-line node/file-extension-in-import
-        const RustCrypto = await import("./rust-crypto");
+        const RustCrypto = await import("./rust-crypto/index.ts");
 
         const rustCrypto = await RustCrypto.initRustCrypto({
             logger: this.logger,
diff --git a/yarn.lock b/yarn.lock
index 19fbe865b1..b530c58e14 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -2278,6 +2278,11 @@ babel-plugin-polyfill-regenerator@^0.6.1:
   dependencies:
     "@babel/helper-define-polyfill-provider" "^0.6.2"
 
+babel-plugin-search-and-replace@^1.1.1:
+  version "1.1.1"
+  resolved "https://registry.yarnpkg.com/babel-plugin-search-and-replace/-/babel-plugin-search-and-replace-1.1.1.tgz#2e5b4488e41d9eba1c220651b1a9b350fdf10915"
+  integrity sha512-fjP2VTF3mxxOUnc96mdK22llH92A6gu7A5AFapJmgnqsQi3bqLduIRP0FpA2r5vRZOYPpnX4rE5izQlpsMBjSA==
+
 babel-preset-current-node-syntax@^1.0.0:
   version "1.0.1"
   resolved "https://registry.yarnpkg.com/babel-preset-current-node-syntax/-/babel-preset-current-node-syntax-1.0.1.tgz#b4399239b89b2a011f9ddbe3e4f401fc40cff73b"