Grohl, 46, who fell off stage at a concert in Sweden, underwent a surgery on Monday.
Dates in Belgium, Edinburgh and London's Wembley Stadium have also been cancelled, reported BBC.
"Doctors have required the cancellation of the remainder of the band's dates in the UK and Europe," said a statement on the band's website.
"After undergoing surgery Monday, Dave's full recuperation time is still to be determined."
The band were two songs into their set at the Ullevi stadium last Friday, when Grohl mistimed a jump onto a ramp and proceeded to fall into the gap between the stage and audience.
Writing on the Foo Fighters website on Tuesday night, Grohl called it "the single most bizarre Foo Fighters show in the entire 20 years of being a band.
"What seemed like a tragedy at first turned into a triumph, and we all walked away with a new sense of appreciation for what we've got."
Posting a photo of the "six metal screws in my leg", he added: "It kills me to say it (but) the doctors have told us to cancel shows.
Glastonbury is yet to announce a replacement headliner for their Friday night line-up, but said in a statement, "We wish Dave Grohl all the best for a full and speedy recovery." It is not the first time organisers have had to make a last-minute change to the top of the bill.
Five years earlier, Basement Jaxx replaced Kylie Minogue - who was forced to pull out after being diagnosed with breast cancer.
In 1995, Pulp played a career-defining headline set after The Stone Roses' guitarist John Squire broke his collar-bone in a biking accident.
