The climate activist group said Reverend Dr Sue Parfitt, 82, and Judy Bruce, an 85-year-old retired biology teacher, entered the library and smashed the glass enclosure around the historic document.
According to Just Stop Oil, the pair then glued themselves to the enclosure holding a sign which read “the government is breaking the law”, and could be heard saying: “Is the government above the law?”
The historic Magna Carta was issued in June 1215 and sought to prevent the king from exploiting his power.
It was sealed in Runnymede by King John.