The incident took place at around 10 p.m. on Thursday night in the Columbia Road Northwest neighbourhood.
Police Commander Stuart Emerman told reporters at the scene that no suspect has been apprehended yet and the incident was still under investigation but they were looking into the possibility it was a drive-by shooting.
The victims - five men and a woman - were shot in the courtyard of an apartment complex.
The condition of at least one of the victims was critical, police said.
Washington Police also reported a second shooting about an hour later on the other side of the city in which at least three people were injured.
There is currently no indication that the two shootings are related, Emerman said.
Shootings, many related to gang violence, are not uncommon in Washington and its metropolitan area.
The city, which has a population of around 700,000, has already recorded 123 homicides so far this year plus another 90 in its metropolitan area, most of them involving firearms.
In 2018, 160 homicides were committed in Washington and 120 in the suburbs for a total of 280.
However, despite being high, this figure is still a far cry from those registered at the start of the 2000s with a peak in 2002 of 262 murders in Washington and 189 in the metropolitan area, for a total of 451.
( With inputs from IANS )