It said the military had declared an alert and activated search and rescue teams.
The C-130 Hercules carried 17 crew members and 21 passengers, including three civilians. The personnel were to check on a floating fuel supply line and other equipment at the Chilean base.
President Sebastián Piñera said via Twitter that he was with his defense and interior ministers at the air force headquarters monitoring developments.
The plane took off at 4:55 p.m. from the southern city of Punta Arenas, which is more than 3,000 kilometers (1,860 miles) from the capital of Santiago. Contact was lost at 6:13 p.m., the statement said.
The air force said late Monday that the weather good at the time contact was lost.
Gen. Eduardo Mosqueira of the Fourth Air Brigade told local media that a search was underway and a ship was in the area where the plane should have been when contact was lost.
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 Monday night.