A large number of smart devices in Internet of Things (IoT) environments communicate via different messaging protocols. Message Queuing Telemetry Transport (MQTT) is a widely used publish-subscribe-based protocol for the communication of sensor or event data. The publish-subscribe strategy makes it more attractive for intruders and thus increases the number of possible attacks over MQTT. In this paper, we proposed a Deep Neural Network (DNN) for intrusion detection in the MQTT-based protocol and also compared its performance with other traditional machine learning (ML) algorithms, such as a Naive Bayes (NB), Random Forest (RF), k-Nearest Neighbour (kNN), Decision Tree (DT), Long Short-Term Memory (LSTM), and Gated Recurrent Units (GRUs). The performance is proved using two different publicly available datasets, including (1) MQTT-IoT-IDS2020 and (2) a dataset with three different types of attacks, such as Man in the Middle (MitM), Intrusion in the network, and Denial of Services (DoS). The MQTT-IoT-IDS2020 contains three abstract-level features, including Uni-Flow, Bi-Flow, and Packet-Flow. The results for the first dataset and binary classification show that the DNN-based model achieved 99.92%, 99.75%, and 94.94% accuracies for Uni-flow, Bi-flow, and Packet-flow, respectively. However, in the case of multi-label classification, these accuracies reduced to 97.08%, 98.12%, and 90.79%, respectively. On the other hand, the proposed DNN model attains the highest accuracy of 97.13% against LSTM and GRUs for the second dataset.