The cricketer apparently popped the question in front of VIP diners at the Road Hole Restaurant in the Old Course Hotel following a romantic meal.
Hurley, who is in Scotland to attend the Alfred Dunhill Links Golf Championship with Warne, accepted his proposal, according to the Daily Mail.
"Shane proposed over dinner and it was fairly public, not a private affair," a source said. "It was a VIP crowd in there this evening. It was residents only, including Dunhill past players.
"He didn't get down on one knee, but when it was announced the other guests in the restaurant stood up and applauded. Everyone there was absolutely delighted."
Previous reports had indicated that Warne was planning to propose to the actress. The pair have been dating since December last year.