The incident, which was not spotted by match officials, occurred in the 38th minute of Manchester United's 1-0 win at St James' Park on Wednesday.
"Both players were charged in relation to an alleged breach of FA Rule E1[a] in that in or around the 38th minute of the fixture they spat at each other," the FA said in a statement.
"Mr Cisse accepted the charge and his suspension consists of six matches, which is the standard penalty for this offence, with an additional one match as he has previously accepted a violent conduct charge this season.
"Mr Evans denied the charge but it was found proven following an Independent Regulatory Commission hearing on Friday."
Neither player has been granted the right to appeal against the sanction and the bans are effective immediately.
The FA's charge was brought after a three-man panel of former referees said both players should have been dismissed for their actions.
Northern Ireland international Evans, 27, will miss fourth-placed United's FA Cup quarter-final against Arsenal on Monday and Premier League games against Tottenham Hotspur, Liverpool, Aston Villa, Manchester City and Chelsea.
Senegalese forward Cisse, 11th-placed Newcastle's top scorer this season, will sit out fixtures against Everton, Arsenal, Sunderland, Liverpool, Spurs, Swansea City and Leicester City.
(Reporting By Tom Hayward. Editing by Ed Osmond)
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