When agents from the Secret Service approached the man around midnight local time, he displayed a firearm.
"An armed confrontation followed, during which our personnel fired shots," the security force states in a statement.
The man, whose injuries are unclear, is believed to have traveled to the capital from the state of Indiana. The Secret Service had received a warning about the man from local police.
No one else was injured in connection with the shooting, which occurred about a block from the White House. US President Donald Trump was in Florida at the time.
The local police announce that they will investigate the incident, but provide no further details.
Corrected: In an earlier version of the text, an incorrect statement appeared about where on the body the man was shot.
