Electronic prescription (E-prescription) is an emerging technology that allows health practitioners (doctors, physicians, pharmacists, or nurses) to electronically transmit prescriptions to pharmacies. E-prescription systems allow doctors to avoid traditional medical practices in which prescriptions are sent manually in handwritten form. Additionally, in cases in which a patient may not be able to collect the medication in person due to physical disabilities, the medications can be delivered to the patient's home directly. Furthermore, payments can also be made online (e.g., using credit cards or bank transfers). However, these distinctive features require a series of guidelines for the successful deployment of the E-prescription system due to stringent legal requirements and privacy regulations. Two major security requirements i.e. confidentiality and authentication need to be addressed. In general, the solution to ensuring confidentiality and authentication lies in the combination of both the encryption and digital signature functions in a single logic step called signcryption. Therefore, in this paper, we present a lightweight and provable secured certificate-based proxy signcryption (CB-PS) scheme for e-prescription systems. The formal security verification uses the Automated Validation of Internet Security Protocols and Applications (AVISPA) tool along with informal security analysis, which authenticates that the proposed CB-PS scheme can potentially be implemented in resource-constrained low-computing electronic devices in E-prescription systems.