The shooting occurred at around 3 a.m. in the 800 block of St. Marys Street, spokesman Lt. Isaac Benabou said.
The 40-year-old male suspect is alert and stable at a hospital. Benabou said the person's injuries are not considered life-threatening.
Officers involved in the shooting were not injured.
Benabou said police are not releasing information on how the shooting occurred until they investigate more.
The Bay City News contributed to this report.