The Springbok was yellow carded after attempting to break up a fight in the Super 14 clash and gesticulated to Roos as he left the field.
On Monday a South African Rugby Union disciplinary tribunal said Burger had acted "in a manner contrary to good sportsmanship".
A statement from the judicial committee, chaired by Jannie Lubbe, said: "The suspension runs from February 23 to March 8 inclusive. He has a right to appeal the sentence.
"During the hearing, Burger conceded that by showing signs after receiving a yellow card, he acted in breach of the law. He strongly denied abusing assistant referee Willie Roos."
Roos was at the centre of controversy a week earlier when the Stormers sent a letter to SA director of referees Andre Watson complaining about his handling of their defeat to the Bulls in the opening round.