The Canadian musician said he had to drop out because he “got sick a few days ago” and doctors have said he is not “physically fit to fly or deliver the performance my fans expect”.
He was due to play gigs in both London and Birmingham.
Kanye West, the other headline act at Wireless Festival, will now headline two nights in London.
In a statement, Drake said: “To my beloved fans, it truly breaks my heart that I won’t be able to perform as planned at Wireless and Roskilde this weekend.
“I got sick a few days ago and although I am on my way to bouncing back, my doctors have made it clear that I am not physically fit to fly or deliver the performance my fans expect and deserve from me.
“I will be focused on resting for a quick recovery.
“I have the best fans in the world and I can’t wait to come back to make more incredible memories together.”
Organizers have confirmed that all three days of Wireless Festival will go ahead as planned in both London and Birmingham.
They said Rudimental would play an extended set on July 4 in Birmingham to compensate for Drake’s absence.
The group will also be joined by “an array of very special guests” who are yet to be announced.
Ticket holders attending the show on Friday in Birmingham will also receive £20 ($32) of “Wireless Credit” upon arrival at the site. This will be redeemable anywhere on site including food, beverages, merchandise and funfair.
Refunds will be available from point of purchase before the event but will not be available at the event, organizers confirmed.
It has moved from the Olympic Park in east London, where it took place last year.
It is based at Finsbury Park in London and Perry Park in Birmingham and this weekend is also the festival’s 10th anniversary.
Other acts performing include Pharrell Williams, Outkast, Tinie Tempah, Basement Jaxx, Ellie Goulding, Wiz Khalifa, Azealia Banks, Robin Thicke, Clean Bandit, Rudimental, John Newman and Angel Haze.
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