The band returned to action only last month after an 11-year absence, kicking off a North American tour with Run The Jewels which had originally been due to start in March 2020.
The US band cancelled their European tour on Thursday, two weeks before they were due to headline the twin UK festivals and play a date in Edinburgh.
A statement said Zack de la Rocha was following “medical guidance”.
It didn’t specify the medical issue, but the 52-year-old singer injured his leg on stage in Chicago in July.
The 1975, made up of Matty Healy, George Daniel, Adam Hann and Ross MacDonald, have not played live in the UK since 2020.
The group, who last played Reading and Leeds in 2019, previously cancelled their 2021 live dates due to the uncertainty surrounding the coronavirus pandemic.
All four of the 1975’s albums have reached number one in the UK. Their fifth is due to be released later this year.
Rage Against The Machine, known for the 1993 anti-authority anthem Killing in the Name, resumed their US tour with de la Rocha performing seated, and will play three more shows in New York this week.
“Then Zack must return home for rest and rehabilitation,” Thursday’s statement said. “The flights, travel time, and rigorous schedule in the UK and Europe are simply too much of a risk for a complete recovery.
“We are so sorry to all of our fans who have waited years to see us and hope to Rage again soon.”