Bishop yelled and cursed at the officer, police said, and told him: "Mind your own (expletive) business."
Police said the officer asked for identification and, when Bishop failed to produce any, moved to arrest him.
Bishop broke free and punched the officer in the face, police said, causing a cut and eye swelling.
The officer, whose name was not released, was treated and released at New York University's Langone Medical Center.
Other officers arrived and hauled Spider-Man away.
Bishop's mother answered the phone at their Brooklyn home late Saturday and said he was not home. She said she was not aware of his work in Times Square or his arrest. Information on Bishop's lawyer was not available.
The arrest of Spider-Man, as police referred to Bishop throughout a matter-of-fact news release, came weeks after the New York City Council said it was considering legislation to regulate the costumed characters in Times Square.
It was the latest in a series of incidents involving men behind the masks.
In the last two years, a man dressed as Cookie Monster was charged with shoving a 2-year-old, a person attired in Super Mario's overalls was accused of groping a woman and an Elmo figure pleaded guilty to disorderly conduct after unleashing an anti-Semitic tirade.
Last month a different Spider-Man was convicted of harassment for a February 2013 episode in which he cursed and complained that a woman did not tip him after posing for a photograph with her children. Phillip Williams later punched the woman in the face and knocked her to the ground — out of self-defense, he said — after she hurled snow at him.
The bill under City Council consideration would require licenses and background checks for costumed performers but copyright issues have held up final approval, since most of the costume wearers are not authorized by the characters' owners.
Police Commissioner William Bratton last week endorsed the measure to combat what he called Times Square's "Elmo issues."