Two others who climbed up a tree inside the Royal Navy base that is home to Britain's strategic nuclear deterrent, 40 kilometres (25 miles) northwest of Glasgow, were being monitored.
The protesters cut through a perimeter fence late Monday night, forcing the base to shut down temporarily.
The spokeswoman said that 12 activists were being held by Ministry of Defence police, while the pair in a tree were under surveillance, allowing the base to reopen.
The Faslane base, on the River Clyde, has long been a focus for anti-nuclear protests. Last January, two activists were detained after getting through one of the outer fences.
A peaceful protest, including the Scottish Campaign for Nuclear Disarmament, is planned for July 4, two days before the start of the Group of Eight summit at the Gleneagles resort in central Scotland.
The 12 arrested Tuesday were expected to appear in court later in the day, a Ministry of Defence spokesman said. They were being questioned at the base on suspicion of a breach of the peace and malicious mischief.
"The arrests follow the activation of an intruder alarm at the base which in turn activated the full number of security measures," the spokesman said. "All of the people were arrested in non-sensitive areas."