The fast progression of Artificial Intelligence (AI) in nearly all fields is equated with a high number of cyber-attacks aimed at ruining AI models. This important challenge of ensuring that data privacy holds in the course of computation remains consistently a big hurdle to the widespread adoption of AI services. The techniques of Privacy-Preserving Artificial AI (PPAI) such as Homomorphic Encryption (HE) make it possible to securely carry out computations on encrypted data. However, conventional HE often suffers from scalability and computational efficiency bottleneck, which are not suitable in resource constrained environments. In order to tackle these challenges, this paper presents a Hybrid Homomorphic Encryption (HHE) technique that makes use of the symmetric cryptography along with HE to strengthen both security and performance for AI services. With that in mind, we present the GuardAI framework, a new framework that is meant to be used for deploying AI applications, where the applications run on resource limited devices. Encrypted data classification is made possible by GuardAI which also ensures data confidentiality of the input data as well as AI models. Finally, we evaluate the performance of the proposed HHE method on a heart disease classification task using electrocardiogram (ECG) signals as an example of data contamination susceptible signals. We demonstrate that the proposed approach provides strong data privacy while resulting in little computational and communication overhead, at least as good as unencrypted inference in classification accuracy. The contribution of this work is to lay the foundation to integrate HHE in AI based cybersecurity solutions, specifically in computationally constrained environments. This work strengthens the security of AI services, by providing both increased privacy and efficiency, and thereby increases their resilience to emerging cyber threats.