The FBI said there was no link to terrorism in the incident.
The motorists, who were not identified, drove to a gate of the secretive government agency in Fort Meade, Md., shortly before 7 a.m. EST. Guards fired on the vehicle after it violated NSA security rules, officials said.
Gordon Johnson, the Federal Bureau of Investigation's special agent in charge for Baltimore, said at a news conference that officials were interviewing the men to determine their motive.
"That's our question one: What put these individuals on this compound earlier this morning?" he said.
Johnson said there was no reason to believe "that there is any nexus to terrorism."
The vehicle had what appeared to be bullet holes in its windshield and extensive front-end damage after crashing into a concrete traffic barrier, according to video of the scene.