Sir Hugh Muir Nelson, KCMG (31 December 1833 – 1 January 1906) was an Australian politician who was Premier of Queensland from 1893 to 1898.

Hugh Nelson obtained a position in a mercantile house, and then took up a pastoral life about six miles out of Ipswich.

In April 1898 when the Byrnes ministry came in, Nelson became president of the Queensland Legislative Council, and in 1903 lieutenant-governor, for both of which positions his fine appearance, tact and grace of manner eminently fitted him.

Nelson had an intimate knowledge of men, and was an excellent parliamentarian with a good grasp of constitutional matters and a keen understanding of financial questions.

He showed himself to be a strong man during the shearers' strike of 1894, but his best work was done as treasurer when he led the colony out of a state of financial chaos.