Healthcare applications are considered as promising fields for wireless sensor networks, where patients can be monitored using wireless medical sensor networks (WMSNs). Current WMSN healthcare research trends focus on patient reliable communication, patient mobility, and energy-efficient routing, as a few examples. However, deploying new technologies in healthcare applications without considering security makes patient privacy vulnerable. Moreover, the physiological data of an individual are highly sensitive. Therefore, security is a paramount requirement of healthcare applications, especially in the case of patient privacy, if the patient has an embarrassing disease. This paper discusses the security and privacy issues in healthcare application using WMSNs. We highlight some popular healthcare projects using wireless medical sensor networks, and discuss their security. Our aim is to instigate discussion on these critical issues since the success of healthcare application depends directly on patient security and privacy, for ethic as well as legal reasons. In addition, we discuss the issues with existing security mechanisms, and sketch out the important security requirements for such applications. In addition, the paper reviews existing schemes that have been recently proposed to provide security solutions in wireless healthcare scenarios. Finally, the paper ends up with a summary of open security research issues that need to be explored for future healthcare applications using WMSNs.