General Alexander Montgomery (c.1721—1785) was an Irish MP for County Monaghan, Ireland.
His father was John Montgomery (died 1733) of Ballyleck, County Monaghan (M.P. for County Monaghan and second son of Colonel Alexander Montgomery (1667–1722)). John had succeeded his father to the Ballyleck Estate when his elder brother Thomas was disinherited for marrying an Englishwoman.
His mother was Mary Coxe, a Maid of Honour to Queen Caroline, wife of King George II of Great Britain. Mary Coxe's father was also the Queen's physician and governor of New Jersey, Dr Daniel Coxe. Montgomery's first cousin was the American Revolution war-hero Major-General Richard Montgomery, a son of the disgraced Thomas.
He was a General of Volunteers. He succeeded his elder brother John Montgomery (died 1741) as an M.P. for County Monaghan in the Parliament of Ireland from 1743 to 1760 and from August 1768 – 1783. He was appointed High Sheriff of Monaghan for 1747–48.