Born near Springfield, Kentucky, McHenry was tutored privately. He studied law. He was admitted to the bar in 1818 and commenced practice in Leitchfield, Kentucky. He was appointed postmaster of Leitchfield October 8, 1819. Major of the Eighty-seventh Regiment, Kentucky Militia, in 1821. He was appointed Commonwealth attorney by Governor Adair in 1822. He moved to Hartford, Kentucky, in 1823. He was appointed Commonwealth attorney by Governor Metcalfe in 1831 and again by Governor Moorehead in 1837. Commissioned colonel in the State militia in 1837. He served as member of the Kentucky House of Representatives from Ohio County, Kentucky in 1840. He was an unsuccessful Whig candidate for election in 1840 to the Twenty-seventh Congress. He was appointed on the board of the Transylvania University in 1843.
Mchenry was elected as a Whig to the Twenty-ninth Congress (March 4, 1845 – March 3, 1847). He was nominated for reelection in 1846, but withdrew his name on the eve of election. He resumed the practice of law. He served as member of the State constitutional convention in 1849 and served as chairman. He moved to Owensboro, Kentucky, in 1854, judge of the circuit court of several counties in 1854. He died in Owensboro, Kentucky, on November 1, 1871. He was interred in Rosehill Elmwood Cemetery.