It is believed that the quartet evaded security by wearing orange marshals uniforms.
They unfurled an "Act Now" banner at Club Corner as the cars set off on the formation lap before they were stopped by track security.
A joint statement issued by Silverstone and Northamptonshire Police read: "During the race, Northamptonshire Police were made aware of four people who had been detained by Silverstone security inside the venue perimeter.
"Officers are working closely with Silverstone Circuit and conducting a full investigation. Four people have been arrested and are in police custody."
The incident will be a concern for Formula One's bosses after Sunday's race took place without fans due to the Covid-19 pandemic.
The 70th Anniversary Grand Prix will also be staged here at Silverstone next weekend.
The environmental group released a statement following Sunday's race.
"Today was an opportunity to remind the world that the climate and ecological crisis hasn't gone away and is intensifying every day," said Donald Bell from Extinction Rebellion Cambridge.
"Although we applaud Formula One for taking the bold steps and pledging to go net zero by 2030, this strong leadership makes a mockery of the EU and UK governments' own 2050 target. It's time the worlds' governments show some leadership of their own."
Sunday's incident is not the first time the Silverstone race has been targeted by protesters. A safety car was deployed in 2003 after an intruder ran across the Hangar Straight, dodging cars at 200mph.
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