The New York Times says Fitz Fullerton was slashed on his hand and jaw after the suspect, Maksim Gelman, forced his way into his cab Saturday.
Fullerton tells the newspaper he was in the hospital when police came to talk to him about the ticket, and handcuffed him.
Police say Fullerton was held for about one hour. He says only later was he asked about the rampage that left four people dead. Fullerton tells the Times he was held for 10 hours.
Gelman was arraigned on second-degree murder and assault charges. He's being held without bail.