He was the second son of the diplomat Sir Nicholas Throckmorton of Beddington, Surrey and was educated at Magdalen College, Oxford.
His sister Elizabeth incurred the Queen's displeasure by secretly marrying Sir Walter Raleigh.
Arthur inherited estates in several counties on the death of his father in 1571 (his elder brother was adjudged a lunatic) and after his marriage opted to reside at Paulerspury in Northamptonshire, where he replaced the medieval manor house and created gardens.
The eldest daughter, Mary, married Sir Thomas Wotton, and inherited the manor of Alderminster from her father.
Their third daughter, Elizabeth, married Richard Lennard, 13th Baron Dacre, and inherited the manor of Cosgrove from her father.