Jason Baum, the university's sports information director, said the 20-year-old man was hurt in a south stairwell at the stadium in Piscataway.
Rutgers public safety officials said the fan sustained head injuries and was taken to Robert Wood Johnson Hospital in New Brunswick, where he was in critical condition.
Baum said the man, whose name was not released, was "not affiliated" with Rutgers, but did not disclose further details.
It also was not immediately clear what caused the accident, which occurred shortly before halftime.
The accident occurred during the Big East conference game between Rutgers and Syracuse, which the visiting Orangemen won 13-10 on a last-minute field goal.