diff --git a/lib/https.js b/lib/https.js
index 1e86e81cf76b15..4849048e20379f 100644
--- a/lib/https.js
+++ b/lib/https.js
@@ -66,6 +66,7 @@ let debug = require('internal/util/debuglog').debuglog('https', (fn) => {
   debug = fn;
 });
 const net = require('net');
+const { Buffer } = require('buffer');
 const { URL, urlToHttpOptions, isURL } = require('internal/url');
 const { validateObject } = require('internal/validators');
 const { isIP } = require('internal/net');
@@ -212,16 +213,18 @@ function getTunnelConfigForProxiedHttps(agent, reqOptions) {
 
 function establishTunnel(agent, socket, options, tunnelConfig, afterSocket) {
   const { proxyTunnelPayload } = tunnelConfig;
+  const maxHeaderSize = tunnelConfig.requestOptions.maxHeaderSize ||
+    getOptionValue('--max-http-header-size');
   // By default, the socket is in paused mode. Read to look for the 200
   // connection established response.
   function read() {
     let chunk;
     while ((chunk = socket.read()) !== null) {
-      if (onProxyData(chunk) !== -1) {
-        break;
+      if (onProxyData(chunk)) {
+        return;
       }
     }
-    socket.on('readable', read);
+    socket.once('readable', read);
   }
 
   function cleanup() {
@@ -239,14 +242,25 @@ function establishTunnel(agent, socket, options, tunnelConfig, afterSocket) {
 
   // Read the headers from the chunks and check for the status code. If it fails we
   // clean up the socket and return an error. Otherwise we establish the tunnel.
-  let buffer = '';
+  let buffer;
   function onProxyData(chunk) {
-    const str = chunk.toString();
-    debug('onProxyData', str);
-    buffer += str;
+    debug('onProxyData', chunk.toString());
+    buffer = buffer === undefined ? chunk :
+      Buffer.concat([buffer, chunk], buffer.length + chunk.length);
     const headerEndIndex = buffer.indexOf('\r\n\r\n');
-    if (headerEndIndex === -1) return headerEndIndex;
-    const statusLine = buffer.substring(0, buffer.indexOf('\r\n'));
+    const headerLength = headerEndIndex === -1 ?
+      buffer.length : headerEndIndex + 4;
+    if (headerLength > maxHeaderSize) {
+      debug(`Proxy response headers exceed ${maxHeaderSize} bytes, cleaning up`);
+      cleanup();
+      const err = new ERR_PROXY_TUNNEL(
+        `Proxy response headers exceeded ${maxHeaderSize} bytes`);
+      afterSocket(err, socket);
+      return true;
+    }
+    if (headerEndIndex === -1) return false;
+    const statusLineEndIndex = buffer.indexOf('\r\n');
+    const statusLine = buffer.subarray(0, statusLineEndIndex).toString();
     const statusCode = statusLine.split(' ')[1];
     if (statusCode !== '200') {
       debug(`onProxyData receives ${statusCode}, cleaning up`);
@@ -286,7 +300,7 @@ function establishTunnel(agent, socket, options, tunnelConfig, afterSocket) {
       });
       tunneldSocket.on('error', onTLSHandshakeError);
     }
-    return headerEndIndex;
+    return true;
   }
 
   function onProxyEnd() {
diff --git a/test/client-proxy/test-https-proxy-request-header-overflow.mjs b/test/client-proxy/test-https-proxy-request-header-overflow.mjs
new file mode 100644
index 00000000000000..2ffc215bafa90a
--- /dev/null
+++ b/test/client-proxy/test-https-proxy-request-header-overflow.mjs
@@ -0,0 +1,45 @@
+// This tests that the proxy server cannot send unbounded incomplete headers
+// while establishing a CONNECT tunnel.
+
+import * as common from '../common/index.mjs';
+import assert from 'node:assert';
+import { once } from 'events';
+import http from 'node:http';
+import { runProxiedRequest } from '../common/proxy-server.js';
+
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+
+const proxy = http.createServer();
+proxy.on('connect', common.mustCall((req, socket) => {
+  socket.write('HTTP/1.1 200 Connection Established\r\n');
+
+  const interval = setInterval(() => {
+    if (socket.destroyed) {
+      clearInterval(interval);
+      return;
+    }
+    socket.write('x'.repeat(100));
+  }, 10);
+  socket.on('close', () => clearInterval(interval));
+  socket.on('error', () => clearInterval(interval));
+}, 1));
+proxy.listen(0);
+await once(proxy, 'listening');
+
+const { code, signal, stderr, stdout } = await runProxiedRequest({
+  NODE_USE_ENV_PROXY: 1,
+  REQUEST_URL: 'https://localhost:1/test',
+  HTTPS_PROXY: `http://localhost:${proxy.address().port}`,
+}, ['--max-http-header-size=1024']);
+
+assert.match(
+  stderr,
+  /ERR_PROXY_TUNNEL.*Proxy response headers exceeded 1024 bytes/,
+);
+assert.doesNotMatch(stderr, /MaxListenersExceededWarning/);
+assert.strictEqual(stdout.trim(), '');
+assert.strictEqual(code, 0);
+assert.strictEqual(signal, null);
+
+proxy.close();