The army said the plane was flying between the southern city of Myeik and Yangon (Rangoon). Search and rescue efforts are under way.
"Communication was lost suddenly at about 1:35 pm [07:05 GMT] when it reached about 20 miles west of Dawei town," the army said in a statement.
There were 106 military personnel and family members and 14 crew on board.
The plane, a Y8 transporter made in China, was half an hour into the short routine flight.
Latest reports suggest that debris has been spotted in the sea by some of the military planes or ships dispatched to the area.
There were no reports of bad weather at that time. The plane was purchased from China in March last year and had logged 809 flying hours, the army said.
Myanmar has seen a number of aircraft incidents in recent years.
In February 2016, the five-member crew of an air force plane died when the aircraft crashed in the capital of Nay Pyi Taw. A few months later, three officers were killed when a military helicopter crashed in central Myanmar.
An Air Bagan commercial aeroplane made an emergency landing in 2012 and burst into flames, killing two people.
Hopes are fading for the 120 people on board a Burmese military plane which has gone missing over the Andaman Sea.