The Liverpool striker, who has the right of appeal, was sanctioned by an FA Independent Regulatory Commission.
Evra told French TV he was racially abused by the Uruguayan on 10 occasions during Manchester United's Barclays Premier League match at Anfield on October 15.
The FA said in a statement: "An Independent Regulatory Commission has found a charge of misconduct against Luis Suarez proven, and have issued a suspension for a period of eight matches as well as fining him £40,000, pending appeal."
The commission's ruling stated: "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; The [penalty] is suspended pending the outcome of any appeal lodged by Mr Suarez against this decision."
The FA confirmed that Suarez's suspension will not start until the outcome of any appeal.
The statement added: "Mr Suarez has the right to appeal the decision of the Independent Regulatory Commission to an Appeal Board. An appeal must be lodged within 14 days of the date of the written reasons for the decision.
"The penalty is suspended until after the outcome of any appeal, or the time for appealing expires, or should Mr Suarez decide not to appeal. The reason for this is to ensure that the penalty does not take effect before any appeal so that Mr Suarez has an effective right of appeal."
The Uruguay striker had strongly denied the accusation and was fully supported by Liverpool.
Evra made the claims immediately after the match at Anfield two months ago, telling French TV station Canal Plus that Suarez 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 Suarez's defence was based on claims that he 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 racist to him. I said nothing of the sort.
"There were two parts of the discussion - one in Spanish, one in English. I did not insult him. It was just a way of expressing myself. I called him something his team-mates at Manchester call him, and even they were surprised by his reaction."
Evra reported his complaint to match referee Andre Marriner, who included it in his report.
Luis Suarez Factfile
1987: Born January 24 in Salto, Uruguay.
2005: Makes professional debut with Montevideo club Nacional, scoring 12 goals in 29 games in his one and only season in South America.
2006: Signs for Dutch side FC Groningen and fires 10 goals in 29 appearances for the club.
2007: February 8 - Makes debut for Uruguay against Colombia and is sent off in the 85th minute.
August - Joins Ajax in a deal reportedly worth 7.5million euros (£6.3million).
2008: Ends debut season in Amsterdam with 17 goals in 33 Eredivisie games.
2009: May - Suarez nets 22 goals in 31 league appearances for Ajax.
November - Part of the Uruguay side which books the final place at the 2010 World Cup in South Africa with a 2-1 aggregate win over Costa Rica.
2010: May - Suarez enjoys his most prolific season in Holland yet, with 35 goals in 33 Eredivisie matches.
June - Suarez scores three goals to help Uruguay reach the quarter-finals but is then sent off for a goal-line handball against Ghana in the last eight. Ghana miss the resultant penalty before Uruguay go on to triumph in a shoot-out.
Without Suarez in the line-up, Uruguay lose to Holland in the semi-finals.
November - Banned for seven matches after being found guilty of biting PSV Eindhoven's Otman Bakkal.
2011: January 28 - Liverpool agree a deal worth up to £22.8million with Ajax for Suarez.
February 2 - Scores on his Liverpool debut in a 2-0 victory over Stoke at Anfield.
October - Manchester United defender Patrice Evra makes an allegation that Suarez racially abused him during the 1-1 draw between Liverpool and United at Anfield on October 15.
November 17 - Suarez is charged by the Football Association with racially abusing Evra following a month-long investigation.
December 20 - The FA ban Suarez for eight matches and fine him £40,000.