Mobile and sensor related technologies are significantly revolutionizing the medical and healthcare sectors. In current healthcare systems, gadgets are the prominent way of acquiring medical services. However, the recent technological advancements in smart and ambient environments are offering users new ways to access the healthcare services without using any explicit gadgets. One of the key challenges in such gadget-free environments is performing secure user authentication with the intelligent surroundings. For example, a secure, efficient and user-friendly authentication mechanism is essential for elderly/disabled people or patients in critical conditions requiring medical services. Hence, modern authentication systems should be sophisticated enough to identify such patients without requiring their physical efforts or placing gadgets on them. This paper proposes an anonymous and privacy-preserving biometrics based authentication scheme for such gadget-free healthcare environment. We performed formal security verification of our proposed scheme using CDVT /AD tool and our results indicate that the proposed scheme is secure for such smart and gadget-free environments. We verify that the proposed scheme can resist against various well-known security attacks. Moreover, the proposed system showed better performance as compared with existing biometrics based remote user authentication schemes.