Well, for MQTT the arduino needs to have WLAN/LAN access to the MQTT broker.
This would be possible for ESP8266 and ESP32 and e.g. the pubsubclient library.
But an Arduino doesn’t have a Ethernet or WiFi chip.
Fine, so you just need to connect the ESP to your WiFi and setup e.g. pubsubclient (https://github.com/knolleary/pubsubclient).
Now you can send and receive MQTT messages with your ESP.
For a quick start, i would create a simple item that displays a text on your sitemap. This item subscribes to a MQTT topic which is sent to your MQTT Broker from the ESP.