The incident happened shortly after 11 p.m. in the southeast part of the district.
Metropolitan Police Department Executive Assistant Chief Ashan Benedict said officers in the area heard gunshots and, as they arrived on the scene, a group of people directed them to those who were shot.
The child was taken to a local hospital, where she was later pronounced dead, he said.
In addition, three men and two women were shot and sustained non-life-threatening injuries, Benedict said.
No arrests have been made, according to Benedict.
"There is too much gun violence still perpetuated in this city," said Benedict, who asked the public to assist in identifying any suspects while authorities continue to investigate. — CNN