Cuthbert was born in Boyle, County Roscommon, Ireland, the eldest son of John Cuthbert. Cuthbert was educated at Drogheda Grammar School, winning the classical medal, and studied law. In 1854 he was admitted a solicitor in Ireland, and the same year left for Victoria, where he was at once admitted to practice. In 1855 he went to Ballarat, and, besides being successful in his profession, became largely interested in mining. He was the original promoter of the Buninyong Gold Mining Company.
In September 1874 Cuthbert was returned to the Legislative Council, unopposed, for the South-Western Province, and in November 1882 was transferred to the new Wellington Province. Cuthbert held the office of Postmaster-General of Victoria in the second Graham Berry Administration from July 1877 to July 1878, when he resigned in consequence of inability to support the Government scheme for Reform of the Council. In March 1880 he joined James Service's Ministry as Commissioner of Customs and Postmaster-General, and held office till the defeat of the Government in the following August. Cuthbert was Minister of Justice under Duncan Gillies from February 1886 to November 1890. He married in May 1863 the second daughter of Mr. Kirby, of Melbourne, and was one of the representatives of Victoria at the Federation Convention of 1891. Cuthbert was Solicitor-General of Victoria from 27 September 1894 to 5 December 1899.
Cuthbert was appointed Knight Commander of the Order of St Michael and St George in the 1897 Diamond Jubilee Honours. Cuthbert died at Ballarat, Victoria, Australia on 5 April 1907.
- Benson, M. Martina. "Cuthbert, Sir Henry (1829–1907)". Australian Dictionary of Biography. Canberra: Australian National University. Retrieved 5 December 2013.
- Mennell, Philip (1892). " Cuthbert, Hon. Henry". The Dictionary of Australasian Biography. London: Hutchinson & Co. Wikisource
- "Cuthbert, Sir Henry". re-member: a database of all Victorian MPs since 1851. Parliament of Victoria. Retrieved 5 December 2013.