Authorities say the victim, identified as 35-year-old Joel Custer, was assaulted by the man while biking across the bridge just before 7 a.m.
He was knocked off his bicycle by the force of the attack, which was apparently unprovoked.
The suspect, identified as 64-year-old Everett Gayle, was half-naked by the time responding police arrived on the bridge.
Officers covered the suspect with clothing and took him to Elmhurst Hospital for evaluation. Custer was taken to New York Presbyterian Hospital with a jaw injury.
Gayle will be charged with assault. He is currently being treated for psychological evaluation.