diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index 04acb5d30f6..66fad34629c 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -295,6 +295,7 @@ const {
 
 const {
   NGHTTP2_CANCEL,
+  NGHTTP2_ENHANCE_YOUR_CALM,
   NGHTTP2_REFUSED_STREAM,
   NGHTTP2_DEFAULT_WEIGHT,
   NGHTTP2_FLAG_END_STREAM,
@@ -886,6 +887,13 @@ function requestOnConnect(headersList, options) {
   // For the first two, emit the error on the session,
   // For the third, emit the error on the stream, it will bubble up to the
   // session if not handled.
+  if (ret === false) {
+    // The session is over its `maxSessionMemory` budget. Only this request is
+    // rejected; the session itself stays usable.
+    this.destroy(new ERR_HTTP2_STREAM_ERROR(
+      nameForErrorCode[NGHTTP2_ENHANCE_YOUR_CALM]));
+    return;
+  }
   if (typeof ret === 'number') {
     let err;
     switch (ret) {
diff --git a/src/node_http2.cc b/src/node_http2.cc
index a6779610ddb..13bf30b4feb 100644
--- a/src/node_http2.cc
+++ b/src/node_http2.cc
@@ -3073,6 +3073,19 @@ void Http2Session::Request(const FunctionCallbackInfo<Value>& args) {
     return;
   }
 
+  // maxSessionMemory is documented to reject new streams while the limit is
+  // exceeded. CanAddStream() enforces that for peer-initiated streams; apply
+  // the same memory check to locally initiated requests so that a session
+  // whose socket is not draining cannot queue frames without bound. Like the
+  // response header check, queued request bodies are not counted, so large
+  // uploads do not prevent unrelated requests on the same session.
+  if (!session->has_available_session_memory(sizeof(Http2Stream),
+                                             /* exclude_outbound */ true))
+      [[unlikely]] {
+    Debug(session, "not submitting request: session memory limit exceeded");
+    return args.GetReturnValue().Set(false);
+  }
+
   Debug(session, "request submitted");
 
   int32_t ret = 0;
diff --git a/src/node_http2.h b/src/node_http2.h
index 4576d5678f0..9f5dddd183f 100644
--- a/src/node_http2.h
+++ b/src/node_http2.h
@@ -832,6 +832,7 @@ class Http2Session : public AsyncWrap,
     uint64_t total = current_session_memory_ + sizeof(Http2Session);
     total += current_nghttp2_memory_;
     total += outgoing_storage_.size();
+    total += outgoing_buffers_.size() * sizeof(NgHttp2StreamWrite);
     return total;
   }
 
diff --git a/test/parallel/test-http2-max-session-memory-client-request.js b/test/parallel/test-http2-max-session-memory-client-request.js
new file mode 100644
index 00000000000..d10eec6f43a
--- /dev/null
+++ b/test/parallel/test-http2-max-session-memory-client-request.js
@@ -0,0 +1,95 @@
+'use strict';
+
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+
+const assert = require('assert');
+const http2 = require('http2');
+const { once } = require('events');
+
+const { NGHTTP2_ENHANCE_YOUR_CALM } = http2.constants;
+
+// maxSessionMemory is documented to reject new streams while the limit is
+// exceeded. Make sure that also holds for requests initiated by a client
+// session, so that a peer that does not read cannot make the client queue
+// frames without bound. As for response headers, request bodies that are
+// queued waiting for flow control are not counted, so a large upload does not
+// prevent unrelated requests on the same session.
+
+async function queuedUploadDoesNotBlockRequests() {
+  // The server never opens its flow-control window, so the upload stays queued
+  // in the client session.
+  const server = http2.createServer({ settings: { initialWindowSize: 0 } });
+  server.on('stream', common.mustCall((stream) => {
+    stream.on('error', () => {});
+  }, 2));
+  server.listen(0);
+  await once(server, 'listening');
+
+  const client = http2.connect(`http://localhost:${server.address().port}`, {
+    maxSessionMemory: 1,
+  });
+  client.on('error', common.mustNotCall());
+  await once(client, 'remoteSettings');
+
+  const uploadArrived = once(server, 'stream');
+  const upload = client.request({ ':method': 'POST', ':path': '/upload' });
+  upload.on('error', () => {});
+  upload.end(Buffer.alloc(4 * 1024 * 1024));
+  await uploadArrived;
+
+  const other = client.request({ ':path': '/other' });
+  other.on('error', () => {});
+  await once(server, 'stream');
+
+  other.destroy();
+  upload.destroy();
+  client.destroy();
+  server.close();
+}
+
+async function manyRequestsAreBounded() {
+  // A peer that accepts the connection and then stops reading. Before the
+  // session memory check, every request was queued regardless of the limit.
+  const server = http2.createServer();
+  server.on('connection', (socket) => setTimeout(() => socket.pause(), 30));
+  server.on('stream', (stream) => stream.on('error', () => {}));
+  server.listen(0);
+  await once(server, 'listening');
+
+  const client = http2.connect(`http://localhost:${server.address().port}`, {
+    maxSessionMemory: 1,
+  });
+  client.on('error', () => {});
+  await once(client, 'connect');
+
+  const total = 30_000;
+  let rejected = 0;
+  for (let i = 0; i < total; i++) {
+    const req = client.request({ ':path': `/${i}` });
+    req.on('error', (err) => {
+      if (err.code === 'ERR_HTTP2_STREAM_ERROR' &&
+          err.message.includes('NGHTTP2_ENHANCE_YOUR_CALM')) {
+        rejected++;
+      }
+    });
+    req.end();
+  }
+  await new Promise(setImmediate);
+
+  assert.ok(rejected > 0, 'expected some requests to be rejected');
+  // Without the check all of the requests (plus the connection preface) were
+  // queued: the number of queued frames grew with the number submitted.
+  assert.ok(client.state.outboundQueueSize < total,
+            `queued ${client.state.outboundQueueSize} of ${total}`);
+  assert.strictEqual(NGHTTP2_ENHANCE_YOUR_CALM, 11);
+
+  client.destroy();
+  server.close();
+}
+
+(async () => {
+  await queuedUploadDoesNotBlockRequests();
+  await manyRequestsAreBounded();
+})().then(common.mustCall());