Spartak fine Argentine duo over late arrival
Spartak coach Valery Karpin also banned the two central defenders from training with the first team for turning up several days late from international duty, the Moscow club said on their website.
Spartak did not say when the pair would be allowed to rejoin their team-mates.
Argentina had a disappointing Copa America as the hosts were knocked out by eventual winners Uruguay in the quarter-finals earlier this month.
Pareja, 27, joined Spartak from Spanish club Espanyol a year ago while 21-year-old Rojo arrived from Argentine first division side Estudiantes six months later.
Spartak, Russia's most successful and popular club with nine league titles between 1992-2001, are in fifth place, 13 points behind leaders CSKA Moscow midway through the season.