The C-130 Hercules was carrying 17 crew members and 21 passengers, including three civilians.
It took off from the southern city of Punta Arenas at 4.53pm on Monday and operators lost contact with it at 6.13pm.
The military said it had declared an alert and activated search and rescue teams.
The personnel were on the way to the country’s base in Antarctica to check on a floating fuel supply line and other equipment.
In a statement on Tuesday, the air force said the plane had not been heard from in more than seven hours and likely would have run out of fuel around 12.40am.
The air force “continues the search in the sector where communication with the aircraft was lost, in order to rescue potential survivors,” the statement said.
Drake’s Passage, where the plane went missing, is infamous for severe weather conditions, including freezing temperatures and ferocious storms.
But on Monday the air force said the weather was good when the plane began its flight, or the mission would not have been carried out.
General Eduardo Mosqueira of the Fourth Air Brigade told local media a search was underway and a ship was in the general area where the plane should have been when contact was lost.
Gen Mosqueira said 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 on Monday night.
Chile’s president, Sebastian Pinera, tweeted to say he was with his defence and interior ministers at the air force headquarters monitoring developments.