Other items taken in the burglary of the West Sussex castle include coronation cups given by Mary to the Earl Marshal, as well as gold and silver items.
Staff were alerted to the break-in late on Friday, May 21, after a burglar alarm went off and police were scrambled to the scene.
A car has since been burnt out and abandoned and is thought to have been involved in the raid.
A Sussex Police spokesman said thieves stole gold and silver items worth in excess of one million pounds.
"Various items have been stolen of great historical significance. These include the gold rosary beads carried by Mary Queen of Scots at her execution in 1587, several coronation cups given by the sovereign to the Earl Marshal of the day, and other gold and silver treasures.
"The rosary is of little intrinsic value as metal, but as piece of the Howard family history and the nation's heritage it is irreplaceable.
"The items were taken by force from a display cabinet along the public route."
A spokesman for Arundel Castle Trustees said: "The stolen items have significant monetary value, but as unique artefacts of the Duke of Norfolk's collection have immeasurably greater and priceless historical importance.
"We therefore urge anyone with information to come forward to the police to assist them in returning these treasures back where they belong."