International standards bodies define Electromagnetic field (EMF) emission requirements that can be translated into control of the base station actual Effective Isotropic Radiated Power (EIRP), i.e., averaged over a sliding time window. In this work we show how to comply with such requirements by designing a water-filling power allocation method operating at the MAC scheduler level. Our method ensures throughput fairness across users while constraining the EIRP to a value that is produced by an outer-loop procedure which is not the focus of our paper. The low computational complexity of our technique is appealing given the tight computational requirements of the MAC scheduler. Our proposal is evaluated against the prior art approaches through massive-MIMO system level simulations that include realistic modeling of physical and MAC level cellular procedures. We conclude that our proposal effectively mitigates EMF exposure with considerably less impact on network performance, making it a standout candidate for 5G and future 6G MAC scheduler implementations.