Henry Bradstreet Cleaves (February 6, 1840 – June 22, 1912) was an American politician and the 43rd Governor of Maine from 1893 to 1897.

Cleaves attained the rank of lieutenant by time he was mustered out of service.

After the Civil War, he returned to Bridgton and was involved in his family's farm as well as in the lumber business.

Leaving the Legislature, he then served as the city solicitor for Portland (1877–1879), and as the Maine Attorney General from 1880 to 1884.

During his administration, problems resulting from the national economic depression in 1893 were dealt with.