A posting on the band’s website says Bono “injured his arm in a cycling spill in Central Park” and will need surgery to repair it.
The posting by guitarist The Edge, bassist Adam Clayton, and drummer Larry Mullen did not say when or how the accident happened.
The bandmates also said they would have to reschedule their planned week-long appearance on the US TV programme The Tonight Show with Jimmy Fallon.
An NBC spokesperson confirmed that U2, who had been booked to appear every day this week, had pulled out.
Just last week, German authorities said Bono’s private plane lost a hatch as it was coming in for a landing at Berlin’s airport.