Governor Hennessy may refer to:
James Hennessy (diplomat) (1923–2024), Governor of British Honduras from 1980 to 1981 John Pope Hennessy (1834–1891), Governor of Labuan, the Gold Coast, Sierra Leone, the Bahamas, Barbados and the Windward Islands, Hong Kong, and Mauritius for various terms between 1867 and 1889