The two activists made it on to the airfield at Stansted airport northeast of London, climate protest group Just Stop Oil said in a statement.
Essex Police said they had arrested two women aged 22 and 28 on suspicion of criminal damage and interference with national infrastructure.
The pair, named by Just Stop Oil as Jennifer Kowalski, 28, and Cole Macdonald, 22, used fire extinguishers filled with orange paint to spray two private jets, the group's statement said.
It said they were demanding that Britain's next government after the July 4 general election legally commit to phasing out fossil fuels by 2030.
In a post on X, Just Stop Oil added: "Jennifer and Cole cut the fence into the private airfield at Stansted where @taylorswift13's jet is parked, demanding an emergency treaty to end fossil fuels by 2030."
The accompanying video showed one of the activists cutting a hole in the fence before spraying the paint over the jets.
Taylor Swift has attracted criticism over her use of private jets.
In 2022, she headlined a list published by British sustainability marketing firm Yard of the "worst private jet CO2 emission offenders" among celebrities.
Her jet flew 170 times in 2022, with total flight emissions for the year reaching 8,293.54 tonnes, or 1,184.8 times more than the average person, Yard said.
The protest at Stansted airport came a day after activists sprayed an orange substance on Stonehenge, the prehistoric UNESCO World Heritage Site in southwest England.
Just Stop Oil said two activists had "decorated Stonehenge in orange powder paint" in a stunt that was roundly condemned by political leaders and heritage bodies.
Police arrested two people on suspicion of damaging the ancient monument.