The plane dumped fuel before landing at about 5:50 p.m., Brown said.
Passengers were put on another jet, which was scheduled to depart for Moscow at about 8 p.m., Delta said.
More than 100 firefighters and other emergency crews went to the airport to await the plane's arrival, the Fire Department of New York said.
Earlier reports of a fire on one of the plane's wings were incorrect, said FAA spokeswoman Holly Baker said.