He was placed on injured reserve Thursday.
Ribeiro underwent a procedure late Wednesday night to repair the contusion, which included a tracheotomy.
Higgins was assessed a two-minute minor penalty on the play.
"It's tough," Stars general manager Joe Nieuwendyk said about the loss of Ribeiro. "Every team faces injuries, but this is one you don't always see. He's an important player for us. We're going to have to pull together in his absence."
Ribeiro is expected to remain at St. Vincent's Catholic Medical Center in Manhattan for a few days while the swelling goes down.
Stars associate athletic trainer Craig Lowry stayed with Ribeiro on Wednesday and Ribeiro's wife, Tamara, has joined him in New York.
The Stars recalled center Warren Peters from the Texas Stars of the AHL.