The crash, involving several vehicles, happened on the southbound carriageway, near the Hindhead tunnel at Bramshott, at about 07:30 GMT on Thursday.
The 32-year-old man was pronounced dead at the scene.
Police said a 33-year-old man from Waterlooville had been arrested on suspicion of causing death by driving without due care and attention.
The road was closed between Thursley and Liphook until early evening while officers investigated the scene.
A cyclist has died after being in a crash with a car on the A3 in Hampshire.