Jose Mourinho's assistant has also been warned over his future conduct and fined £30,000 after admitting two Football Association charges and requesting a hearing.
Faria was charged with two counts of improper conduct after he attempted to confront referee Mike Dean towards the end of a 2-1 defeat on Easter Saturday.
Faria had to be dragged away by Mourinho and was accused of two rule breaches - failing to leave the technical area when asked and insulting the fourth official.
Mourinho was also charged for his post-match comments about ref Dean, whose decision to award Sunderland an 83rd-minute penalty prompted Faria's reaction.
The Chelsea manager has since denied the charge and is awaiting a hearing.
An FA statement read: "Following an Independent Regulatory Commission hearing, Chelsea coach Rui Faria has been given a six-match stadium ban with immediate effect, subject to any appeal, after he admitted two breaches of FA Rules.
"The first breach was that Faria used abusive and/or insulting words towards the fourth official during Chelsea's game against Sunderland on 19 April 2014.
"The second breach was that his behaviour following the match referee's request that he leave the technical area amounted to improper conduct.
"Faria, who requested a non-personal hearing, was also fined £30,000 and warned as to his future conduct."
Faria could yet appeal his suspension, which is longer than the three-game stadium ban handed to Newcastle boss Alan Pardew following his head-butting incident with Hull's David Meyler.
It's all about context. In the land where punching a horse is not unusual behaviour, merely nutting someone is a minor offence.- lee