Francis Matthew John Baker (1903 – 28 March 1939) was an Australian politician and vice-president of the State Service Union. Baker was born in Bundaberg, Queensland. A member of the Federal Labor Party, he unsuccessfully ran for office for the Queensland seat of Oxley in the 1928 federal election, being beaten by James Bayley of the Nationalist Party. He made a second run for the seat in 1929, and narrowly lost to Bayley. In 1936, Baker led a proposal for Australian parliamentary proceedings to be broadcast on radio. Baker is buried in South Brisbane Cemetery.