Rapper Bobby Vylan, of rap punk duo Bob Vylan, led crowds attending the festival in chants of "free, free Palestine" and "death, death to the IDF" on Saturday.
Avon and Somerset Police said video evidence would be assessed by officers "to determine whether any offenses may have been committed that would require a criminal investigation."
The Israeli Embassy to the UK said on social media it was "deeply disturbed by the inflammatory and hateful rhetoric expressed on stage at the Glastonbury Festival."
Health Secretary Wes Streeting on Sunday condemned the band's actions as "appalling".
He told Sky News the BBC and festival organisers had to answer questions about how the comments were broadcast live to millions.
The government said Culture Secretary Lisa Nandy has spoken to the BBC director general about Bob Vylan's performance.
The BBC said it issued a warning on screen about "very strong and discriminatory language" during the live stream.
Glastonbury is Britain's biggest summer music festival and draws some 200,000 music fans each year to Worthy Farm in southwest England. Almost 4000 acts perform on 120 stages.
Festival organisers said on Instagram that Vylan's chants "very much crossed a line."
"We are urgently reminding everyone involved in the production of the Festival that there is no place at Glastonbury for antisemitism, hate speech or incitement to violence."
"With almost 4000 performances at Glastonbury 2025, there will inevitably be artists and speakers appearing on our stages whose views we do not share, and a performer's presence here should never be seen as a tacit endorsement of their opinions and beliefs," it said.
Saturday's festival lineup also included Irish-language rap group Kneecap, which gave an impassioned performance for tens of thousands of fans despite criticism by British politicians and a terror charge for one of the trio.
Liam Óg Ó hAnnaidh, who performs under the stage name Mo Chara, has been charged under the Terrorism Act with supporting a proscribed organisation for allegedly waving a Hezbollah flag at a concert in London in November.
The rapper, who was charged under the anglicized version of his name, Liam O'Hanna, is on unconditional bail before a further court hearing in August.
The group has faced criticism for lyrics laden with expletives and drug references, and for political statements, especially since videos emerged allegedly showing the band shouting "up Hamas, up Hezbollah" and calling on people to kill politicians.
On Saturday, band members led the audience in chants of "Free Palestine" and "Free Mo Chara".
They also aimed an expletive-laden chant at UK Prime Minister Keir Starmer, who has said he didn't think it was "appropriate" for Kneecap to play Glastonbury.
with PA
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