The shooting happened at around 7:30 p.m. Monday night in the Milestone Center located on North Frederick Road.
The victim, identified as 24-year-old Mariam Folashade Adebayo, was taken to a local hospital where she died from her injuries.
Witnesses told FOX 5's Alexandra Limon they heard two gunshots and then a Target employee rushed over to the victim and called 911.
Police say the suspect, identified by police as 27-year-old Donald Wayne Bricker, Jr., fled from the parking lot in a white Ford Range pickup truck before officers arrived. Witnesses described his vehicle to police and an officer located the suspect's truck and began a pursuit of the vehicle.
Police arrested Bricker, Jr. in the 15800 block of Darnestown Road after he was involved in a single-vehicle collision.
The Bricker, Jr. was taken to the hospital with non-life-threatening injuries from the crash. A handgun was located at the scene of the accident.
The shooting was domestic-related. Bricker, Jr. and Adebayo were in a relationship with each other, according to police.
Montgomery County police are investigating the shooting as a homicide.