What we know about the suspectpublished at 05:40 British Summer Time
Police have named Elias Rodriguez as the sole suspect at a news conference.
The 30-year-old Chicago man was seen "pacing back and forth outside of the museum" where the shooting took place, they said.
He approached a group of four people and produced a handgun, at which point he shot both victims.
Rodriguez is now being held in custody and DC Mayor Bowser has said there is "no active threat in our community".