A third person was slightly wounded, possibly by breaking glass, but did not need further treatment, police said.
The mayor also said the attack appeared to be the work of one person but that officials were examining all possibilities.
Joseph Persichini, assistant director in charge of the Washington DC's field office for the Federal Bureau of Investigation (FBI) said authorities have dispatched officials to "a suspect's" home to check his computer, the Associated Press news agency reported.
He said they were investigating the incident as a possible hate crime or as domestic terrorism.
"People were screaming and ducking down getting on the floor, getting under benches"
Angela Andelson, shooting eyewitness
Angela Andelson, visiting the museum from San Francisco, told AFP she heard up to five shots fired during the incident.
"I heard the first one. When I turned and looked there were maybe two to four more shots that I heard," said Andelson.
"People were screaming and ducking down getting on the floor, getting under benches."
Stephanie Geraghty, 28, who was also at the museum, told Reuters the shooter appeared to be a white male carrying a silver gun.
"I heard the first shot, it sounded like something had been dropped from the upper stories down," she said.
"The next two came really fast ... at that point, everyone took off. [There was] chaos, running."
The museum was closed for the day following the shooting while nearby streets were cordoned off by police.
The building normally has a heavy security presence with guards positioned both inside and outside, while visitors are also required to pass through metal detectors at the entrance, and bags are screened, the Associated Press news agency said.
However Kathy Lanier, DC's chief of police, said at a news conference following the shooting that the alleged shooter opened fire as soon as he entered the building.
The White House said Barack Obama, the US president, was "saddened" by the shootings.
The embassy of Israel in Washington DC condemned the attack in a statement and said it was "closely following" the situation.
Robert Gibbs, the White House spokesman, said White House officials are receiving regular updates from the FBI, the Homeland Security Council and the White House
situation room on the shooting.
The museum, which is about 500 metres from the White House, is a popular tourist attraction drawing about 1.7 million visitors each year.