Wireless Body Area Networks (WBANs) have been extensively deployed to offer remote patient monitoring that facilitate timely diagnosis and medication. This has greatly helped reduce costs and stress on the limited healthcare resources. However, the exchange of sensory patient data across wireless public communication media exposes the communication process to a myriad of security threats. To curb these security challenges, past research work has deployed techniques such as identity-based and public key cryptosystems to develop schemes for this environment. Nevertheless, the complex mathematical computations in majority of these schemes render them inefficient for sensors. In this current work, we utilize an amalgamation of asymmetric cryptography and user biometrics to develop a robust authentication protocol for WBANs. The famous Burrows–Abadi–Needham (BAN) logic is then deployed to formally analyze the security posture of the developed scheme, with results indicating that it offers secrecy and reliability of the negotiated session keys. In addition, the informal security analysis shows that it is robust against typical WBAN attacks such as impersonation and privileged insiders. From the performance perspective, our protocol incurs the least communication and computation costs.