Sir Henry Harpur, 5th Baronet (c 1708 – 7 June 1748) was an English baronet and politician.
He was the oldest son of Sir John Harpur, 4th Baronet, of Calke Abbey, and his wife Catherine, daughter of Thomas Crew, 2nd Baron Crew. He was educated at Brasenose College, Oxford.
Harpur was a Member of Parliament (MP) for Worcester from 1744 to 1747, and for Tamworth from 1747 until his death in 1748, aged about 40. He was succeeded in the baronetcy by his son Henry (c.1739–1789).
His daughter Caroline married the Scottish MP Adam Hay.