Despite his multiple injuries, the surgeon is confident the star will make a "full recovery".
He added: "He will require intensive and progressive therapy, however a full recovery is expected."
U2 were forced to cancel their week-long residency on The Tonight Show Starring Jimmy Fallon following the smash, and the Irish rockers took to their website to thank the host for his "understanding" in the circumstances.
A statement read: "It looks like we will have to do our Tonight Show residency another time - we're one man down.
"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."
The accident came just a few days after the One singer cheated death when a door fell off his private jet as he flew to Berlin, Germany.
A source said after the terrifying accident last Wednesday: "He was extremely lucky, the plane could have gone down."
A full list of Bono's injuries:
1. Left facial fracture involving the orbit of his eye.
2. Left scapula (shoulder blade) fracture in three separate pieces.
3. Left compound distal humerus fracture where the bone of his humerus was driven though his skin and the bone was in six different pieces.
4. One day later, he had surgery to his left hand to repair a fracture of his 5th metacarpal (finger bone).
- Bang! Showbiz