Faria had to be restrained by Jose Mourinho on the touchline after reacting furiously when referee Mike Dean awarded a penalty to the Black Cats.
Faria, who has also been fined £30,000, had admitted two charges of misconduct.
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."