diff --git a/src/module_wrap.cc b/src/module_wrap.cc
index f164d801b65864..6f9fc3286deacc 100644
--- a/src/module_wrap.cc
+++ b/src/module_wrap.cc
@@ -58,6 +58,7 @@ ModuleWrap::ModuleWrap(Environment* env,
   object->SetInternalField(kURLSlot, url);
   object->SetInternalField(kSyntheticEvaluationStepsSlot, undefined);
   object->SetInternalField(kContextObjectSlot, undefined);
+  MakeWeak();
 }
 
 ModuleWrap::~ModuleWrap() {
diff --git a/test/es-module/test-vm-synthetic-module-leak.js b/test/es-module/test-vm-synthetic-module-leak.js
new file mode 100644
index 00000000000000..34cfc92501994d
--- /dev/null
+++ b/test/es-module/test-vm-synthetic-module-leak.js
@@ -0,0 +1,24 @@
+'use strict';
+
+// Flags: --experimental-vm-modules --max-heap-size=20
+// This tests that vm.SyntheticModule does not leak.
+// See https://github.com/nodejs/node/issues/44211
+
+require('../common');
+const vm = require('vm');
+
+let count = 0;
+async function createModule() {
+  const m = new vm.SyntheticModule(['bar'], () => {
+    m.setExport('bar', new Date().toISOString().repeat(1e6));
+  });
+  await m.link(() => {});
+  await m.evaluate();
+  count++;
+  if (count < 30000) {
+    setImmediate(createModule);
+  }
+  return m;
+}
+
+createModule();
diff --git a/test/known_issues/test-vm-source-text-module-leak.js b/test/known_issues/test-vm-source-text-module-leak.js
new file mode 100644
index 00000000000000..0404e04f7df0f8
--- /dev/null
+++ b/test/known_issues/test-vm-source-text-module-leak.js
@@ -0,0 +1,23 @@
+'use strict';
+
+// Flags: --experimental-vm-modules --max-heap-size=20
+// This leaks because of the strong persistent v8::Module references
+// from ModuleWrap. We need replace that with a GC-aware ModuleWrap ->
+// v8::Module reference to fix this.
+
+require('../common');
+const vm = require('vm');
+
+let count = 0;
+async function createModule() {
+  const m = new vm.SourceTextModule('export default "hello".repeat(1e5)');
+  await m.link(() => {});
+  await m.evaluate();
+  count++;
+  if (count < 30000) {
+    setImmediate(createModule);
+  }
+  return m;
+}
+
+createModule();