The C-130 Hercules, carrying 17 crew members and 21 passengers, crashed after it took off from the southern city of Punta Arenas.
Chile's air force said on Tuesday one of its cargo planes had crashed with 38 people on board after going missing for more than 12 hours and said that a rescue team was searching for possible survivors.
The Hercules C-130 aircraft took off at 1955 GMT on Monday from the southern city of Punta Arenas in Chilean Patagonia and was heading to a base in Antarctica, but operators lost contact with the plane an hour later.
The air force said in a statement it had yet to locate the military cargo plane or determine whether there were any survivors, but said it had concluded the plane must have crashed given the number of hours it had been missing.
The plane had been carrying 17 crew members and 21 passengers, including three civilians, the air force said, adding that its rescue team was scouring the area "where it lost communication with the plane, with the goal of rescuing possible survivors".
The region where the plane disappeared is a vast, largely untouched ocean wilderness of penguin-inhabited ice sheets off the edge of the South American continent.
Eduardo Mosqueira of the Fourth Air Brigade told local media that the aircraft would have been about halfway to the Antarctic base when it lost contact.
No emergency signals had been activated, he said.
He said the plane, whose pilot had extensive experience, had been scheduled to return Monday night.
The plane had been travelling to perform logistical support tasks for the maintenance of Chilean facilities at the Antarctic base, the air force said.