A member of the Scottish Murray family, David's father, Robert Murray, was the Laird of Abercairney, near Crieff; his mother was Katherine Murray, a daughter of William Murray of Tullibardine. David had an older brother, William, and younger brothers, Mungo of Craigie, John Minister of Dunfermline and Leith, Andrew, Quintigern, and James. His two sisters were Nicola(s), who married Robert Douglas of Spott Lord Belhaven, who had been Prince Henry's Stable Master, and Anne, who married William Moncrieff of Moncrieff.
William Murray, David's elder brother, was brought up at Stirling Castle with the young James VI of Scotland. Annabel Murray, Countess of Mar, who shared responsibility for the King at Stirling, was the aunt of their father. The London "Water Poet" John Taylor made a point of visiting his great friend William during his Pennyles Pilgimage to Scotland in 1618.
David left no heirs; Mungo's sons are known by the name 'Moray', the eldest was the soldier and mathematician Robert Moray, and a younger son, William Moray of Dreghorn, Master of Works in Scotland to Charles II.