For one thing the mask will dampen the acoustic field considerably, it acts as a barrier (its primary job). So the effect would be similar to trying to sing or talk with your hand over your mouth, or through a closed window. The sound just won't be as strong. I would suspect that the effect would be frequency dependent meaning that different frequencies in your voice would be dampened by a different amount thus changing the timbre of the voice. Lastly, the mask will fill with warm air and that could change the way your throat feels when you sing, increase congestion in the nose, and also make it hard to inhale deeply to get proper support.
Acoustically I am not sure there is anything you can do to compensate, other than turning up the volume and maybe playing with an EQ at the PA console. My vocal coach sings in a Catholic church for the Archdiocese where she lives. They were doing full Church choirs for an ordination ceremony with all singer 6 ft apart and wearing masks. The masks were altered to have a much bigger box around the face, almost like the plague masks you see. That helped with some of the issues but the performance was still a bit muffled.