Sir Henry Moore, 1st Baronet (7 February 1713 – 11 September 1769) was a British colonial administrator who served as the governor of New York from 1765 to 1769, when he died in office.

Moore agreed with Sears and the colony's assembly to suppress the Stamp Act, and gained additional goodwill by reducing military fortifications within the city.

However, during the next few years, he actively used military force to suppress rural riots by tenants of the large estate owners.

This did not seem to bring him any increased difficulty in governing, for two reasons: that the Sons of Liberty also feared the introduction of rural problems into the city, believing that they should be the only ones to use riots as a bargaining tactic; and that the assembly at the time was dominated by the patroons, or large estate owners.

Moore left with the respect of almost all the colony's leadership, the only exception being certain religious fundamentalists angered by his efforts to create a theatre or playhouse.

He was succeeded in the baronetcy by his thirteen-year-old son John Henry Moore, 2nd Baronet, who died in 1780 aged 23.