In future fifth-generation and beyond radio systems, access points equipped with massive antennas will be deployed to support the increased communication demands. As a result, radio environments will become more dense and users will be exposed to higher electromagnetic field (EMF) radiation from wireless devices than today. This paper proposes to take preemptive action toward protecting the public health from potential EMF-related ill effects by examining radiation-aware solutions for future green wireless communication systems from the radio resource scheduling perspective. Our efforts focus on correlating the transmit power levels of the wireless system with the operands used to express the EMF dosimetry metrics known as maximum permissible exposure and specific absorption rate. In addition, we formulate power minimization problems subject to the maximum permissible exposure and specific absorption rate safety standards, and the individual user quality-of-service demands to derive convex optimization-based solution of dynamic subcarrier allocation and adaptive power management. The simulation results confirm that our green solution reduces significantly the user exposure to radiation, while providing the required quality of service. We expect that our findings can kick off new research directions for controlling the public exposure to radiation from wireless devices in dense networks toward safer fifth-generation communication systems. © 2018 John Wiley & Sons, Ltd.