The man believed to have shot President John F Kennedy was interred in the pine coffin for almost 20 years.
He was exhumed in 1981 as his widow wanted to verify that it was him inside the coffin, and then reburied in a new casket in the same Texas cemetery.
Auction officials say bidding for the item will start at $1,000 (£640) but they expect it to go much higher.
“There’s just a lot of interest in Kennedy and anything to do with his assassination,” said Laura Yntema, manager for Nate D Sanders auction house.
The exhumation of his body in 1981 was designed to lay to rest one of these theories – namely, that the man who was buried was a Soviet agent who had taken Oswald’s identity to carry out the killing.
The auction in Los Angeles also includes instruments that were used to embalm Oswald, his death certificate, an Easter card he sent to his brother, and a section of the car seat on which President Kennedy was sitting when he was shot.
Insert ‘sold to the man behind the grassy knoll‘ puns here please.