diff --git a/packages/pg-protocol/src/parser.ts b/packages/pg-protocol/src/parser.ts
index f900193d7..1ad4e3abd 100644
--- a/packages/pg-protocol/src/parser.ts
+++ b/packages/pg-protocol/src/parser.ts
@@ -199,7 +199,7 @@ export class Parser {
       case MessageCodes.CopyData:
         return this.parseCopyData(offset, length, bytes)
       default:
-        assert.fail(`unknown message code: ${code.toString(16)}`)
+        return new DatabaseError('received invalid response: ' + code.toString(16), length, 'error')
     }
   }
 
diff --git a/packages/pg/test/integration/gh-issues/2627-tests.js b/packages/pg/test/integration/gh-issues/2627-tests.js
new file mode 100644
index 000000000..83e09b910
--- /dev/null
+++ b/packages/pg/test/integration/gh-issues/2627-tests.js
@@ -0,0 +1,63 @@
+'use strict'
+const net = require('net')
+const helper = require('./../test-helper')
+
+const suite = new helper.Suite()
+
+const options = {
+  host: 'localhost',
+  port: Math.floor(Math.random() * 2000) + 2000,
+  connectionTimeoutMillis: 2000,
+  user: 'not',
+  database: 'existing',
+}
+
+// This is the content of the packets sent by a MySQL server during the handshake.
+// Those were captured with the `mysql:8.0.33` docker image.
+const MySqlHandshake = Buffer.from(
+  'SgAAAAo4LjAuMjgAHwAAAB4dKyUJZ2p6AP///wIA/98VAAAAAAAAAAAA' +
+    'AAo1YiNJajgKKGkpfgBjYWNoaW5nX3NoYTJfcGFzc3dvcmQAIQAAAf+EBC' +
+    'MwOFMwMUdvdCBwYWNrZXRzIG91dCBvZiBvcmRlcg==',
+  'base64'
+)
+
+const serverWithInvalidResponse = (port, callback) => {
+  const sockets = new Set()
+
+  const server = net.createServer((socket) => {
+    socket.write(MySqlHandshake)
+
+    // This server sends an invalid response which should throw in pg-protocol
+    sockets.add(socket)
+  })
+
+  let closing = false
+  const closeServer = (done) => {
+    if (closing) return
+    closing = true
+
+    server.close(done)
+    for (const socket of sockets) {
+      socket.destroy()
+    }
+  }
+
+  server.listen(port, options.host, () => callback(closeServer))
+}
+
+suite.test('client should fail to connect', (done) => {
+  serverWithInvalidResponse(options.port, (closeServer) => {
+    const client = new helper.Client(options)
+
+    client
+      .connect()
+      .then(() => {
+        done(new Error('Expected client.connect() to fail'))
+      })
+      .catch((err) => {
+        assert(err)
+        assert(err.message.includes('invalid response'))
+        closeServer(done)
+      })
+  })
+})