Fly-half Russell, 28, was sent off with 10 minutes left of his side's first victory in Paris since 1999 on Saturday (AEDT).
"The red card had been issued for an infringement of Law 9.12 (A player must not physically or verbally abuse anyone. Physical abuse includes, but is not limited to, biting, punching, contact with the eye or eye area, striking with any part of the arm (including stiff-arm tackles), shoulder, head or knee(s), stamping, trampling, tripping or kicking)," the Championship said.
"In terms of mitigation, the Disciplinary Committee gave credit for Mr Russell's prompt acceptance that his actions had constituted foul play and been worthy of a red card, his disciplinary record, his attitude to the disciplinary process before and during the hearing, and his clear remorse (shown by his response to Mr Dulin on the pitch), and reduced the suspension by three weeks so that the final period of suspension is three weeks," it added.
Russell has the right to appeal and will be able to return to play on either April 19 or 26 depending on Racing 92's progress in the European Champions Cup.
Racing hosts Scottish side Edinburgh in the Champions Cup last 16 this Monday before a potential last eight tie against the winner of Bordeaux-Begles against Bristol Bears next weekend.
The Parisian side will host local rival Stade Francais on 18 April in the French top-flight before travelling to Toulouse a week later.