It happened in the parking lot of the Duke Forest Place business complex in the 3300 block of Chapel Hill Boulevard around 3:15 p.m.
The victims have been identified as 40-year-old Millicent Lavon Blair-Arnett and 45-year-old Anthony Carl Arnett. Police said they had been married to each other and divorced a few years ago. They had two children together.
Court documents revealed Blair-Arnett took out a protective order against her ex-husband over alleged domestic violence.
When police arrived, they found Millicent Blair-Arnett lying in the parking lot. She was pronounced dead at the scene.
Anthony Arnett shot himself as officers arrived on the scene. He was taken to a local hospital where he was pronounced dead a short time later.
Blair-Arnett worked as a speech pathologist in the building where she was shot.
Arnett's mother told ABC11 that she believes her son just "snapped." The couple had been involved in a custody battle for five years. Arnett apparently filed new paperwork on Tuesday alleging his ex-wife had been sabotaging their custody agreement.