It happened Saturday around 1:19 a.m. on the city’s east side.
The incident injured a 66-year-old woman, who was shot, and a 52-year-old woman who was beaten, Fox 2 Detroit reported.
The shooting victim was in stable condition at the hospital.
The victims were overpowered after answering a knock at the door, according to the station.
Police said the intruder made off with the older woman’s wallet.
They described the suspect as having on a black hooded sweater in addition to the clown mask.