Police said the 49-year-old driver complained of jaw pain and redness in the neck area and was taken to a hospital.
It wasn't clear from his tweets whether the specific allegation that Baldwin wanted to refute was that he punched the other man or some other aspect of the story. His publicist said she had no comment.
Baldwin was released from the local police precinct in Manhattan's Greenwich Village neighborhood after about two hours. He was ordered to appear in court Nov. 26.
Baldwin, the star of former television sitcom "30 Rock" and current host of "Match Game," plays President Trump on "Saturday Night Live" and recently started a talk show on ABC.