This work considers the problem of energy efficiency maximization in a RIS-based communication link, subject to not only the conventional maximum power constraints, but also additional constraints on the maximum exposure to electromagnetic radiations of the end-users. The RIS phase shifts, the transmit beamforming, the linear receive filter, and the transmit power are jointly optimized, and two provably convergent and low-complexity algorithms are developed. One algorithm can be applied to the general system setups, but does not guarantee global optimality. The second algorithm is provably optimal in a notable special case. The numerical results show that RIS-based communications can ensure high energy efficiency while fulfilling users' exposure constraints to radio frequency emissions.