The 25-year-old said yesterday on ITV's Daybreak that he might have to flee to an island to escape all the new-found fame.
"I'm going to live as a Tibetan monk in a monastery somewhere," he joked. "We're going to start an island somewhere."
The first film in the fantasy fiction franchise is based on the hugely popular novels by Cassandra Clare.
The movie follows the tale of a teenage girl who goes on a life-changing quest after her mother is attacked and taken by a demon.
Sheehan, who stars alongside Lily Collins and Jamie Campbell Bower, says they have been blown away by the mania surrounding the film.
"We've experienced some of the hysteria first-hand. We went to a big mall appearance in Los Angeles recently and we were met by about 1,500 screaming, weeping fans."
The Mortal Instruments: City Of Bones follows New York teen Clary Fray (Lily Collins), who discovers that she has the powers of half-angel, half-human beings called shadowhunters.
Sheehan plays Clary's human friend, Simon, who gets caught up in a battle between good and evil when her mother is kidnapped by a man in search of the mysterious Mortal Cup.
The Irish actor has already signed up to the second film of the franchise, City Of Ashes, which begins production in late September.