The Internet of Things (IoT) enabled technology will be adopted to develop smart cities, electronic commerce, electronic learning, electronic health, and other aspects of online activities. IoT enabled pervasive and wide connectivity to many objects and services. Therefore, it is easy to target IoT and cloud malware infection. Thus, cybersecurity is an essential problem to build robust IoT systems. This paper leverages the recent developments of the swarm intelligence (SI) algorithms combined with the advances of deep neural networks to build an efficient intrusion detection system for IoT-cloud based environments. First, deep neural networks are used to obtain optimal features from the IoT IDS data. Then, an efficient feature selection technique is proposed based on a recently developed SI optimizer called Capuchin Search Algorithm (CapSA). The performance of the developed model, called CNN-CapSA, is tested with four IoT-Cloud datasets, namely, NSL-KDD, BoT-IoT, KDD99, and CIC2017. Moreover, we consider extensive empirical comparisons to other optimization algorithms using several classification performance measures. The outcomes verified that the developed approach has a competitive performance overall datasets.