It happened at Kobelt Airport in Wallkill, Ulster County, about 80 miles north of New York City.
Officials from the FAA said the plane went off the end of the runway into a wooded area around 9:20 p.m.
According to a woman who works at a restaurant at the airport, the plane was headed to Farmingdale, Long Island.
Authorities said two people suffered serious injuries. Two other passengers suffered minor injuries.