The 31-year-old star said the speech problem left her feeling isolated at times when she was 7-year-old.
Blunt recalled that it was her teacher who advised her to pretend being someone else to deal with the problem.
"It was the most intuitive thing, and he was right: the only way I could speak fluently was to be someone else," the actress said.
"It alienates you in some ways if you have trouble communicating. It wasn't that I got bullied horribly about it, although kids definitely had a go sometimes. It comes back if I'm tired or stressed," she revealed.
The film is set in the near future where an alien race has invaded the Earth and has defeated the world's military units. Blunt plays the role of Special Forces warrior Rita Vrataski who guides Major William Cage (Cruise), a military officer to a combat a mission against the aliens.
The Warner Bros film releases in India on June 6.