The multipurpose arena built in 2018 is home to Mystics and also serves as a practice faculty for the Washington Wizards NBA team.
There were no public events scheduled at the arena on Friday, and a police spokesman said the shooting did not appear to be related to the arena. No other details of the shooting were available.
D.C. police are also investigating a shooting Thursday night in the Anacostia neighborhood of Southeast Washington that left one man dead and two others injured.
That shooting occurred shortly before 9:30 p.m. in the 1500 block of V Street SE, near the Frederick Douglass National Historic Site.
Police identified the man who was slain as David Christian Spencer Jr., 41, of Southeast Washington. He was pronounced dead at the scene.
Two other men were taken to a hospital and treated for injuries police described as not life threatening. No arrests were made, and police did not release other details.