Uruguay international Suarez was found guilty of misconduct after using "insulting words" towards Evra during the game on October 15, including a reference to the France defender's colour.
The ban is suspended pending the outcome of any appeal lodged by Suarez after an FA Independent Regulatory Commission "found a charge of misconduct against Luis Suarez proven".
The FA announced the decision against Suarez, who has repeatedly denied the allegations, on its website after a hearing that began on December 14 at an undisclosed location in north-west England.
The commission said: "Mr Suarez used insulting words towards Mr Evra during the match contrary to FA Rule E3(1). The insulting words used by Mr Suarez included a reference to Mr Evra's colour within the meaning of Rule E3(2).
"Mr Suarez shall be warned as to his future conduct, be suspended for eight matches covering all first team competitive matches and fined the sum of 40,000 pounds."
Suarez said on Twitter: "Today is a very difficult and painful day for me and my family. Thanks for all the support."
Liverpool manager Kenny dalglish tweeted: "Very disappointed with today's verdict. This is the time when Luis Suarez needs our full support. Let's not let him walk alone."
The three-man FA commission said it will provide written reasons for its decision in due course following which Suarez will have 14 days to appeal.
Liverpool said in a statement the club was surprised and disappointed with the decision adding: "We find it extraordinary that Luis can be found guilty on the word of Patrice Evra alone.
"No-one else on the field of play - including Evra's own Manchester United team-mates and all the match officials - heard the alleged conversation between the two players in a crowded Kop goalmouth while a corner-kick was about to be taken.
"Nothing we have heard in the course of the hearing has changed our view that Luis Suarez is innocent of the charges brought against him and we will provide Luis with whatever support he now needs to clear his name."
EVRA COMPLAINT
Evra, 30, made the complaint immediately after United's 1-1 draw at Liverpool but investigations into the case before the formal proceedings took two months to prepare.
He reported his concerns to referee Andre Marriner, who included it in his match report.
Evra also made the allegations against 24-year-old Suarez in an interview with Canal Plus, telling the French TV station the Uruguayan had used a racist insult to him "at least 10 times".
Evra said: "There are cameras. You can see him [Suarez] say a certain word to me at least 10 times."
Both players spoke to FA officials during the investigation and there have been suggestions Suarez was unaware language that is acceptable in Uruguay is viewed as racist in Europe.
Suarez told Uruguayan media last month: "There is no evidence I said anything rac
