The statement from band members Edge, Adam and Larry did not give details on the injury or the upcoming surgery.
However, they said they were cancelling a planned weeklong "residency" on late night's the "Tonight Show" on US network NBC.
"It looks like we will have to do our Tonight Show residency another time -- we're one man down," the musicians wrote.
"Bono has injured his arm in a cycling spill in Central Park and requires some surgery to repair it.
"We're sure he'll make a full recovery soon, so we'll be back! Much thanks to Jimmy Fallon and everyone at the show for their understanding."