Healthcare applications store private user data on cloud servers and perform computation operations that support several patient diagnoses. Growing cyber-attacks on hospital systems result in user data being held at ransom. Furthermore, mathematical operations on data stored in the Cloud are exposed to untrusted external entities that sell private data for financial gain. In this paper, we propose a privacy-preserving scheme using homomorphic encryption to secure medical plaintext data from being accessed by attackers. Secret sharing distributes computations to several virtual nodes on the edge and masks all arithmetic operations, preventing untrusted cloud servers from learning the tasks performed on the encrypted patient data. Virtual edge nodes benefit from cloud computing resources to accomplish computing-intensive mathematical functions and reduce latency in device–edge node data transmission. A comparative analysis with existing studies demonstrates that homomorphically encrypted data stored at the edge preserves data privacy and integrity. Furthermore, secret sharing-based multi-node computation using virtual nodes ensures data confidentiality from untrusted cloud networks.