The incident occurred during half-time of the FIFA World Cup second-round clash between Brazil and Chile on June 28, which the hosts won on penalties after a 1-1 draw.
Pinilla claims he was punched by Paiva, who insists the fracas was nothing more than pushing and shoving.
FIFA initially suspended Paiva for one match, meaning he was unable to fulfil his usual duties in Brazil's quarter-final victory over Colombia, while making it clear a stronger punishment could follow.
And Paiva will now be forced to sit out the remainder of the tournament, after his suspension was extended to three games, including the Colombia fixture, by FIFA's disciplinary committee.
Article 48 of FIFA's disciplinary code stipulates a ban of "at least two matches for assaulting (elbowing, punching, kicking etc) an opponent or a person other than a match official."
Brazil face Germany on Tuesday with a place in the final, against Argentina or the Netherlands, at stake.
