The shooting happened inside a car in front of three children, ages 6, 4, and 1, along the 200 block of Copley Road, investigators said.
Police say the 34-year-old woman was picking up two of the children she shared with the alleged gunman when he opened fire. The woman was found inside the vehicle.
Officers say the man then turned the gun on himself.
The woman, whose name has not been released, was pronounced dead at the scene. The father is hospitalized in critical condition, according to police.
The circumstances leading up to the shooting remain under investigation.