The SUV, believed to be rented, drove through the NSA gate at about 7:00 am (1200 GMT), and NSA security officials followed official protocols for handling such an incident, he said.
"We believe there is no indication that anything more than an isolated incident of what happened here today this morning", he said, stressing it was not terror related.
Mr. Johnson did not say who fired the shots - whether the occupants of the auto or security personnel - as the F.B.I. continued its investigation.
US President Donald Trump attends a roundtable discussion on the MS-13 gang in the Cabinet Room of the White House in Washington, DC.
The NSA said several individuals were transported to a local hospital, adding that the "injuries are not attributable to gunfire". Video footage from WRC-TV showed police surrounding a handcuffed man sitting on the ground near the vehicle.
However, local media reported that three people were injured and one arrested, but this has not been confirmed.More news: New Lego Kessel Run Millennium Falcon Unveiled
"Weapons were discharged in the course of the incident, which remains under investigation", the agency said in a statement. The vehicle appears to have crashed into a security barrier, ramming it through a large fence. "Meade", and the White House offered thoughts and prayers with those who have been affected, spokeswoman Lindsay Walters said.
A law enforcement source said the FBI's Baltimore office was handling the investigation but it was "too soon to tell" whether it was an attack.
The FBI ruled out on Wednesday terrorism as a motive when a motorist tried to drive into the headquarters of the US National Security Agency in Washington.
Authorities closed down a nearby highway, causing long traffic delays during the morning commute, news reports said. In addition to the hospitalized driver, whose condition officials did not reveal, an NSA police officer and a bystander were hurt, although not seriously. More details will be released as they become available - on the probe, that is, not God's response.
But drivers have taken the wrong exit before and ended up at the tightly secured gates.
In March 2015, one person was killed and another seriously wounded after driving a vehicle up to the NSA's gate, ignoring commands to stop.