Mack, a property broker who lived with his Thai wife in the eastern city of Phatthaya, had been missing since 4 July.
Eight Thai soldiers have also been killed in the fighting so far this week, with 80 more wounded, it said.
Some 10,000 Burmese people have fled to Thailand to escape fierce fighting between the military and units of a powerful ethnic armed group since Wednesday, Thai authorities said.
There are approximately 30,000 Thai workers in Israel, according to the foreign ministry.