Gloucestershire Police said they received a call about “three suspicious vehicles” travelling towards RAF Fairford at 00:45 BST on Sunday.
Five men were later arrested by its officers near Whelford, a village around two miles (3.2km) south-east of the base.
A bomb disposal team was also deployed to the village to examine a number of vehicles, police said, around which a 400m (1,312ft) cordon is in place.
Aerial pictures showed a remote-controlled robot approaching two stationary white vans in a wooded area, though its use has not been confirmed by police.
Counter Terrorism Policing (CTP) is leading the investigation into the incident.
The US military said it was “working closely” with its UK counterparts “to monitor this situation, minimise impacts and ensure the safety of US personnel, their families, and the local community”.
There has been a large emergency service presence in the area since the early hours of Sunday, which Gloucestershire Police Temporary Chief Constable Maggie Blyth said would remain over the next few days.
Blyth told a news conference on Sunday evening that the force would continue to assist CTP and liaise with other national partners.
She also said she would leave any declaration of a “terrorist incident” to CTP.
