Conflict in Shan State, in the northeast bordering China, has displaced at least 50,000 people, with trade routes cut off and several towns seized since an anti-junta offensive launched last month by three ethnic minority insurgent groups.
China has called for all sides to cease hostilities.
The insurgent alliance says it has seized more than 100 army posts. Assaults on towns have also taken place in Sagaing region, in central Myanmar, west of Shan State.
Hundreds of foreign workers, many of whom rights activists say are victims of human trafficking, are trapped by the fighting, including citizens of Vietnam and of Thailand.
The Thai foreign ministry said on Saturday that 200 of its nationals were waiting to be evacuated “as soon as possible when the situation permits”.
The KNDF said on its Facebook page it shot down the jet on Saturday using heavy machine guns and its members were searching for the pilots.
Reuters could not verify the information.
News outlet Mizzima on its Facebook page posted images of what it said were the abandoned helmet and parachute of one of the pilots.