Danielle Brand, 26, says she suffered a broken rib in the alleged altercation, which took place in Roslyn Heights, Long Island.
Brand told police that Cumia, 54, pinned her against a wall and strangled her when she attempted to flee after the pair argued. She said Cumia stomped on her hand, injuring it.
Brand was treated at a hospital.
"Mr. Cumia emphatically denies the allegations brought against him, and is optimistic that when the truth comes out, he will be exonerated," said his attorney, Alan J. Schwartz, in a statement.
"This morning, he entered a plea of not guilty to all charges and was released without bail, and directed to appear back in court in January. Simply put, things are not always what they appear to be, and this case is a perfect example of that."
Cumia is accused of strangulation and assault, among other charges.
A video uploaded to the live streaming site Periscope
appears to show Brand describing her injuries and Cumia asking her to leave his home. She alleged that Cumia smashed her cell phone and pulled a landline from the wall when she tried to call for help.
No bail was set and Cumia was released. The judge asked that he stay away from Brand.
Cumia was once part of the controversial Opie and Anthony team with Gregg "Opie" Hughes. He was fired from the show, which airs on SiriusXM, in 2014 after a series of racially charged tweets.
The firing took place after an incident in which Cumia took photographs in Times Square. An African-American woman objected to being photographed and Cumia claimed he was assaulted.
In a series of tweets -- later deleted -- he called the woman an "animal pig face worthless meat sack" and other comments, many with profane language.
He was fired soon after.
"Those remarks and postings are abhorrent to SiriusXM, and his behavior is wholly inconsistent with what SiriusXM represents," the satellite radio company said in a statement at the time.
The show has continued with Jim Norton in Cumia's place and has been titled "Opie with Jim Norton" since Cumia's departure.
Cumia now hosts "The Anthony Cumia Show"