Bass player Ted Dwane, 28, underwent an operation for a blood clot on the brain about two weeks ago.
The folk rock band's keyboard player Ben Lovett told the Radio Times the musician has recovered and is "going to be OK."
"We're going to get back out on that stage at Glastonbury as four brothers and do what we do," Lovett said.
The BBC said the band is to close the festival's main stage Sunday, along with fellow headliners The Rolling Stones and Arctic Monkeys.
2014: The Year in Music [PHOTOS]