A cover wrap will surround the newspaper's second section, TMoS 2, on Sunday May 10.
It features a puzzle that conveys the main focus of the film -- the hunt through Rome against the clock.
Readers will be invited to solve four questions relating to the accompanying map.
They will then be directed online, where they must solve the fifth and final question in no more than three minutes to be in with a chance of winning a trip to Rome.
Marcus Rich, the Mail on Sunday's managing director, said: "The 'Angels & Demons' cover wrap is yet another example of how, in the face of tough advertising conditions, the Mail on Sunday is being proactive in delivering creative solutions to clients, which can engage readers over and above straight display campaigns.
"In committing to solve the puzzle, readers are reminded of the key messaging for the film -- that it's a thrilling, action packed race against time, full of suspense and intrigue."
'Angels & Demons', starring Tom Hanks and Ewan McGregor, is the long awaited follow-up to 'The Da Vinci Code'. Both movies are based on books by Dan Brown.
Stuart Williams, deputy managing director and marketing director of Sony Pictures Releasing UK, said: "The overall media campaign has been constructed to convey both the stature and event nature of the films release and the cover wrap on TMoS 2 reflects and amplifies this positioning."
'Angels & Demons' will be released in cinemas across the UK on May 14.
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