Fordham said in a statement the diagnosis had not been confirmed by lab tests but mumps seemed the most likely disease, the New York Daily News reported.
Twelve of the cases were at Fordham's campus in the Bronx and one at the Lincoln Center campus in mid-town Manhattan, the New York Daily News reported. Five of the cases, including the Manhattan one, were reported Thursday.
A Fordham employee told the newspaper that all of the sick students at the Bronx campus live in dormitories. Officials said all of the sick students have either gone home or have been isolated from others.
People with mumps can infect others for two days before they show symptoms and five days after the symptoms clear up.
The university requires incoming students to have been vaccinated against mumps and a number of other common infectious diseases.
"Mumps in college-age men and women usually runs its course without any lasting effects," Fordham said in a statement. "Nonetheless, the University is trying to see what connection there might be among the affected students while stepping up the frequency and intensity of cleanings in communal bathrooms."