Fairfax police later identified the woman as Katherine A. Martell, 30, and the man as Christopher D. Brooks, 30. Police said they were not married but had a child together, who was safe with a family member.
The episode was called in by a UPS driver who was making deliveries to the nine-story building, Lt. John Lieb said. No one else was hurt in the incident.
The attack was over in seconds. Brooks, driving a white Nissan Rogue, struck Martell near the front entrance of the building at 3101 South Manchester St. Lieb said Brooks got out of the Rogue, shot Martell at least once and then shot himself.
It was not immediately known how many shots were fired or whether Martell was killed by the SUV or in the shooting.
Both people were pronounced dead at the scene.
Fairfax homicide and crime scene detectives were continuing to work outside the building Tuesday afternoon. It was not known whether the pair lived in the complex.
Dana Hedgpeth contributed to this report.