According to the Chilean Air Force, the plane was heading to Antarctica to conduct logistical work.
A Chilean military aircraft has disappeared from radars on Monday, the Chilean Air Force said in a statement.
"The Chilean Air Force reports that this afternoon a C-130 Hercules aircraft of the Aviation Group #10 took off at 04:55 p.m. and lost radio contact at 06:13 p.m [21:13 GMT]", the Monday release says.
The plane was carrying 38 people on board - 17 crew members and 21 passengers.
A state of alert has been declared, and rescue teams have been activated by the authorities.
The aircraft was travelling from Chabunco Air Base in the city of Punta Arenas, in Southern Chile, to the President Eduardo Frei Montalva Antarctica Air Base.
It was transporting personnel to operate an oil pipeline supplying fuel to the base.