Sergio Boscariol and defender Lucas Manuel Leiva have been suspended from football after they were involved in a fight inside Gimnasia's VIP box after Sunday's top-flight game.
The bans were given by the government of the Buenos Aires province.
The Argentine FA suspended 15 players after a brawl in January's friendly.
Gimnasia are seventh in Zone A of the first division with 10 points from seven matches and Estudiantes are third in Zone B with 13 points.
The winners of the two zones meet in the final in May.
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Violence has marred yet another clash between long-standing Argentine rivals Gimnasia and Estudiantes, this time involving a club director and player.