The Pegasus Airlines jet was carrying 171 passengers and six crew members from Izmir province in the west when it crashed at Sabiha Gokcen airport.
The Boeing 737 was trying to land in heavy tailwinds and rain.
The airport was closed and flights diverted after the accident.
Turkish media said the majority of people on board were Turkish but there were also about 20 foreign nationals.
Istanbul Governor Ali Yerlikaya said: "Unfortunately, the Pegasus Airlines plane couldn't hold on the runway due to poor weather conditions and skidded for around 50-60m [164-196ft]."
He said the plane then fell between 30 and 40 metres off the end of the runway.
Health Minister Fahrettin Koca confirmed a Turkish citizen had died and 157 other people had been injured. He said none of the wounded people were in a critical condition.