Police said nearby residents had been evacuated from their homes.
The British government gave authorisation to the US to use RAF Fairford to carry out strikes on Iranian missile sites attacking ships in the Strait of Hormuz.
Iran's Revolutionary Guards warned in July any base used in strikes would be a legitimate target.
A Reuters eyewitness said on Sunday armed police had blocked access to the main gate of the base, while equipment had been positioned in front of access points and residents of a nearby village were evacuated to a leisure centre.
About 30 emergency vehicles, including police cars, ambulances and fire engines, were stationed in the village of Fairford near the base.
"A number of properties are currently being evacuated in the Whelford area following the declaration of a major incident," Gloucestershire police said in a statement, referring to a village near the air base.
"It follows the arrest of several men on suspicion of offences under the Explosives Act.
"The army's specialist explosive ordnance disposal team are currently examining a number of vehicles."
Police said they believed the incident was now contained.
The British government said Prime Minister Andy Burnham was being updated about the incident, adding "it would be inappropriate to comment further whilst investigations are ongoing".
A spokesperson for the US Air Force declined to discuss specific force protection measures.
"The 501st Combat Support Wing and our fellow UK-based Wings remain vigilant and will take appropriate actions to ensure the safety and security of our US service members, civilians, contractors, and their families," the spokesperson said.
"We constantly assess a variety of factors that determine what measures we institute or modify to protect our installations, our people and their families."
Britain said in July its armed forces were ready to protect the country from any attack after Iran's Revolutionary Guards issued a warning not to allow US bombers to fly from Fairford.
British ministers have also briefed critical infrastructure providers on the threat posed by Russia, with the government increasingly concerned about possible sabotage operations and cyberattacks.
Russia denies mounting hybrid attacks on Western nations.
