Police say the incident began in a convenience store near Lansing, where the suspect - named as Sean Ruis - attacked a 77-year-old man who had challenged him for not wearing a mask.
They say Ruis fled the scene in a car.
He was later pulled over by a female deputy sheriff, who opened fire when Ruis lunged towards her.
Michigan State Police released footage of the confrontation in a residential area in the Lansing suburb of Delta early on Tuesday.