Pitt was due to appear in the country for a pre-release screening of the blockbuster film. A statement issued by Paramount explained that the cancellation was due to "ongoing events in Brazil".
Protests began in Brazil last week over plans to increase public transport fares, as well as poor living standards and anger over the increasing cost of hosting next year's football World Cup and the 2016 Rio Olympics.
Paramount also expressed solidarity with the Brazilian people during the time of crisis.
He also hinted that World War Z sequels could be produced if the first is a box office hit.