The local NBC News affiliate reported two damaged vehicles were seen outside the installation's gate about 20 miles northeast of Washington, and that emergency workers attended to an injured man and put him into an ambulance.
An NSA spokeswoman had no immediate comment. Spokesmen for Fort Meade and Anne Arundel County Police referred questions to the spy agency.
NBC television footage showed a large police presence and at least one damaged vehicle.
The Washington Post said police at Fort Meade, a U.S. Army base in Anne Arundel County, Maryland, confirmed that the incident happened on the NSA side of the installation but gave no other details.
In a post on Twitter, the county's police department referred questions to the NSA and Fort Meade, adding that it was "not involved at this point."