Melvin Ernest Thompson (May 1, 1903 - October 3, 1980) was a politician from the U.S. state of Georgia.

Thompson was born in Millen, Georgia. He graduated from Emory University in 1926. Thompson worked in education, first as a principal, moving all the way up to assistant school superintendent. Thompson was a supporter of Governor Ellis Arnall and he was the executive secretary and state revenue commissioner.

In 1946, Thompson ran for the newly created position of Lieutenant Governor. Arnall supported another candidate. Thompson won the primary with less than thirty percent of the vote.

Governor-elect Eugene Talmadge died in December 1946 and the Georgia state constitution was vague on who would be sworn in to replace him. Thompson felt that as the Lieutenant Governor-elect, he should become the Governor. But the state legislature was controlled by Talmadge supporters. They invoked a clause in the Georgia state constitution which allowed for the legislature to pick between the second and third place candidates. The people who finished second and third were two write-in candidates, James V. Carmichael and Eugene's son, Herman E. Talmadge. The legislature selected Herman Talmadge to become the Governor.

Thompson and Arnall both claimed the office of Governor. Arnall renounced his claim to support Thompson.

The Georgia state Supreme court ruled that Thompson was the legitimate governor and that the legislature had violated the state constitution by selecting Talmadge. Thompson's achievements as Governor include raising salaries for teachers. He was defeated by Talmadge in a special election in 1948.

Thompson ran for Governor again in 1950 against Talmadge, again in 1954, and he ran for the United States Senate against Talmadge in 1956. After his defeat in 1956, Thompson retired to Valdosta, Georgia where he worked as a realtor.