Investigators said the weapon believed to have been used by the man was a revolver found near park benches at the scene.
The shooting occurred in a busy section of the Parkway near several museums. Police said there were initial plans to begin shutting down nearby museums, but the shooting happened before those measures could be put in place.
Authorities have not publicly identified the man. Investigators said he was not speaking to officers during the encounter.
Police said they are still working to determine what led to the incident.
The investigation remains ongoing.