Network life time and hence device life time is one of the fundamental metrics in wireless body area networks (WBAN). To prolong it, especially those of implanted sensors, each node must conserve its energy as much as possible. While a variety of wake-up/sleep mechanisms have been proposed, the wake-up radio potentially serves as a vehicle to introduce vulnerabilities and attacks to WBAN, eventually resulting in its malfunctions. In this paper, we propose a novel secure wake-up scheme, in which a wake-up authentication code (WAC) is employed to ensure that a BAN Node (BN) is woken up by the correct BAN Network Controller (BNC) rather than unintended users or malicious attackers. The scheme is thus particularly implemented by a two-radio architecture. We show that our scheme provides higher security while consuming less energy than the existing schemes.