diff --git a/lib/internal/vm/module.js b/lib/internal/vm/module.js
index ce2350f6cd16..0f901c460340 100644
--- a/lib/internal/vm/module.js
+++ b/lib/internal/vm/module.js
@@ -17,6 +17,7 @@ const {
   PromiseReject,
   PromiseResolve,
   SafePromiseAllReturnArrayLike,
+  SafeSet,
   Symbol,
   SymbolToStringTag,
   TypeError,
@@ -332,7 +333,10 @@ class SourceTextModule extends Module {
     }));
   }
 
-  async [kLink](linker) {
+  async [kLink](linker, linkedModules = new SafeSet()) {
+    if (linkedModules.has(this)) {
+      return;
+    }
     this.#statusOverride = 'linking';
 
     // Iterates the module requests and links with the linker.
@@ -358,7 +362,7 @@ class SourceTextModule extends Module {
             throw new ERR_VM_MODULE_LINK_FAILURE(`request for '${specifier}' resolved to an errored module`, module.error);
           }
           if (module.status === 'unlinked') {
-            await module[kLink](linker);
+            await module[kLink](linker, linkedModules);
           }
           return module[kWrap];
         });
@@ -368,6 +372,7 @@ class SourceTextModule extends Module {
     try {
       const modules = await SafePromiseAllReturnArrayLike(modulePromises);
       this[kWrap].link(modules);
+      linkedModules.add(this);
     } catch (e) {
       this.#error = e;
       throw e;
diff --git a/test/parallel/test-vm-module-link-linked-deps.js b/test/parallel/test-vm-module-link-linked-deps.js
new file mode 100644
index 000000000000..179ee0f8c4a4
--- /dev/null
+++ b/test/parallel/test-vm-module-link-linked-deps.js
@@ -0,0 +1,77 @@
+// Flags: --experimental-vm-modules
+
+'use strict';
+
+const common = require('../common');
+const vm = require('vm');
+const assert = require('assert');
+
+// This test verifies that `module.link(linker)` does not link a dependency
+// again when it has already finished linking before another module
+// requests it.
+
+// Regression of https://github.com/nodejs/node/issues/66938
+
+const sources = {
+  './index.js': `
+        import foo from "./foo.js";
+        import shared from "./shared.js";
+        export default { foo, shared };
+    `,
+  './foo.js': `
+        import shared from "./shared.js";
+        export default "foo";
+    `,
+  './shared.js': `
+        import leaf from "./leaf.js";
+        export default leaf;
+    `,
+  './leaf.js': `
+        export default "leaf";
+    `,
+};
+
+const moduleCache = new Map();
+
+function getModuleInstance(identifier) {
+  let module = moduleCache.get(identifier);
+
+  if (!module) {
+    module = new vm.SourceTextModule(sources[identifier], {
+      identifier,
+    });
+    moduleCache.set(identifier, module);
+  }
+
+  return module;
+}
+
+async function test() {
+  const module = getModuleInstance('./index.js');
+  const requests = [];
+
+  await module.link(async (specifier, referrer) => {
+    requests.push([specifier, referrer.identifier]);
+    // Delay `./foo.js` so that `./shared.js` finishes linking before
+    // `./foo.js` requests it.
+    if (specifier === './foo.js') {
+      await new Promise((resolve) => setImmediate(resolve));
+    }
+    return getModuleInstance(specifier);
+  });
+
+  await module.evaluate();
+  assert.strictEqual(module.namespace.default.foo, 'foo');
+  assert.strictEqual(module.namespace.default.shared, 'leaf');
+
+  // Assert that `./shared.js` is not linked again for `./foo.js`.
+  assert.deepStrictEqual(requests, [
+    // [specifier, referrer]
+    ['./foo.js', './index.js'],
+    ['./shared.js', './index.js'],
+    ['./leaf.js', './shared.js'],
+    ['./shared.js', './foo.js'],
+  ]);
+}
+
+test().then(common.mustCall());