The bullet dented a panel on the Wall of Honor, the Washington Post reported. The wall lists the names of 209,145 blacks who enlisted in the Union forces during the war.
Police said two groups of young people, one in a car and the other in the street, began firing at each other outside the museum Thursday night. No one was injured and no arrests have been made.
Spent shell casings and the remains of two panels from a bus shelter shattered by gunfire were scattered in front of the Metro station, the Post said.
Frank Smith, the museum's director, said the neighborhood in Northwest Washington is safe and there have been no other incidents of gunfire in the 20 years since the museum opened.
"Anything can be fixed," Smith said. "And we will fix this. It's a national monument. It can't stay like this for long."
One of the soldiers honored at the memorial is first lady Michelle Obama's great-great-grandfather, Caesar Cohen. He joined the 128th Regiment, United States Colored Infantry, after running away from a South Carolina plantation.