The singer repeatedly recited Mrs May's "strong and stable" election slogan during the band's headline set on the Pyramid Stage.
He chanted the phrase during a rendition of Myxomatosis and later muttered: "See you later, Theresa, shut the door on the way out."
At one point the crowd broke into chanting "Oh, Jeremy Corbyn" to the tune of the White Stripes' Seven Nation Army.
Glastonbury 2017: The best pictures from the festival Sat, June 24, 2017 REUTERS 1 of 19
Revellers dance as Craig David performs on the Pyramid Stage at Worthy Farm in Somerset during the Glastonbury Festival
See you later, Theresa, shut the door on the way out.
Radiohead's appearance marked 20 years since the band's heavily criticised 1997 show at the Somerset festival and the release of hit album OK Computer.
Their return prompted mixed political reactions from the crowd as some festival-goers held up banners in protest against the group's decision to perform in Tel Aviv.
While some waved Palestinian flags, one banner read: "Israel is an apartheid state. Radiohead, don't play there."
Glastonbury festive: Thom Yorke jabbed at Theresa May during Radiohead's set
But the British rockers proved a hit with the audience, and they delighted fans with nostalgic renditions of hit tracks No Surprises, Creep and Karma Police.
The band also treated fans to renditions of Street Spirit, Exit Music (For A Film) and Fake Plastic Trees.
Earlier in the day, Hollywood star Johnny Depp apologised for joking about assassinating US President Donald Trump.
The Hollywood actor courted controversy on Thursday night at Cineramageddon - a drive-in cinema on the Somerset site.
Glastonbury audiences cheered as Yorke told Mrs May to 'shut the door on the way out'
He told the crowd: "I think he needs help and there are a lot of wonderful dark, dark places he could go.
"It's just a question - I'm not insinuating anything.
"By the way, this is going to be in the press. It will be horrible.
"I like that you are all a part of it.
"When was the last time an actor assassinated a president?
"I want to qualify, I am not an actor. I lie for a living.
British rockers proved a hit with the audience and delighted fans with nostalgic renditions of hits
"However, it has been a while and maybe it is time."
In a statement to People magazine, Depp said: "I apologise for the bad joke I attempted last night in poor taste about President Trump.
"It did not come out as intended, and I intended no malice. I was only trying to amuse, not to harm anyone."
He made a second appearance at the festival on Friday when he joined Kris Kristofferson for a live performance on the main Pyramid Stage.
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Local residents in nearby Pilton all get a free ticket to the festival
The festival kicked off when Joy Division and New Order bassist Peter Hook led a minute's silence on stage to remember those who died in the Manchester and London attacks and the Grenfell Tower fire.
Hook's daughter was at the Ariana Grande gig at Manchester Arena on May 22 and was taken to hospital, where she spent time on crutches after being trampled.
Elsewhere, Elbow played an unannounced gig at The Park Stage - delighting thousands of fans with hits including The Bones Tf You.
The 7.30pm Friday slot had been marked as TBA in the festival line-up.