The FA found the Manchester United defender guilty of improper conduct.
A United statement called the ban "excessive" and Evra will miss four matches commencing from 22 December. Chances are they will appeal the decision anyway.
Chelsea were fined £25,000 for failing to ensure an employee conducted himself in an orderly fashion. The FA said charges that groundsman Sam Bethell had used racially abusive language towards Evra after the match could not be proven.
Manchester United left a statement on their website: "Manchester United note the announcement from the FA and are disappointed with the decision and in particular consider the sanctions against Patrice Evra excessive. Manchester United and Patrice will consider all options once there has been an opportunity to digest the full reasons for the decision. There will be no further comment."
The hearing in London finished on Friday and was attended by officials from both clubs, with the cases being heard separately by the FA's regulatory commission. Evra and his team-mates were asked to move while warming down, sparking the row after last season's 2-1 league defeat in April. Evra, Gary Neville, Park Ji-Sung, Danny Wellbeck, John O'Shea and Paul Scholes - who did not feature in the match - were running on the field in a warm-down about 30 minutes after the final whistle when the trouble broke out.
The Frenchman and Bethell were pictured having a confrontation following the incident, with Bethell raising a fist towards Evra while being held back by two Chelsea staff members.