The club reacted swiftly on Thursday following the conclusion of Anelka's independent regulatory commission hearing.
Anelka was also fined B£80,000 for an aggravated breach of Football Association rules and ordered to attend an education programme. He has the right to appeal and his legal team has confirmed he is considering that option.
West Brom said in a statement on their website: "The club has suspended Nicolas Anelka pending the conclusion of the FA's disciplinary process and the club's own internal investigation."
Anelka was charged after performing the gesture, which has been described as racist and anti-Semitic, after scoring for the Baggies at West Ham on December 28.
The two charges the 34-year-old faced - that the gesture was abusive and/or indecent and/or insulting and/or improper, and that it included a reference to ethnic origin and/or race and/or religion or belief - were both found proved.
West Brom, who allowed Anelka to play for them during the investigation, added in their statement: "West Bromwich Albion treats very seriously any such allegation which includes any reference to ethnic origin and/or race and/or religion and/or belief."
Anelka's hearing at the Grove Hotel in Watford this week was conducted by an independent regulatory commission, which concluded that Anelka had not intended the gesture to be anti-Semitic.
The committee's ruling therefore effectively means players can be sanctioned for behaviour that is widely viewed as racist or discriminatory even if they had not meant it to be so.
That follows the 2011 case of Liverpool striker Luis Suarez, who was found guilty of racially abusing Patrice Evra even though he argued the words he used were not racist in his home country Uruguay.
An FA statement read: "An independent regulatory commission has found an aggravated breach of FA rule E3 against Nicolas Anelka proven and has issued a five-match suspension and a fine of B£80,000, pending appeal."
It added: "So far as the basis for our finding on Charge 2 is concerned, we did not find that Nicolas Anelka is an anti-Semite or that he intended to express or promote anti-Semitism by his use of the quenelle."
Anelka and West Brom are now awaiting written reasons for the panel's decision. Once received, Anelka will have seven days to exercise his right of appeal.
Anelka had denied the gesture had any anti-Semitic meaning and said it was a signal in support of his friend, the French comedian Dieudonne M'bala M'bala, who first brought the quenelle to prominence.
A statement from the player's legal advisers Brown Rudnick LLP read: "Nicolas Anelka is pleased that the FA regulatory commission has found him not to be an anti-Semite and that he did not intend to express or promote anti-Semitism by his use of the quenelle gesture.
"He is now waiting to receive the commission's full reasons for their decision before considering whether or not to appeal.
"Nicolas Anelka has been advised not to make any further comment while the proceedings are ongoing."
The FA's ban is suspended for seven days to allow for written reasons to be received.
Anelka, however, will not be playing for the club in the meantime following West Brom's own action.
The club's statement added: "The club acknowledges that the FA panel 'did not find that Nicolas Anelka is an anti-Semite or that he intended to express or promote anti-Semitism by his use of the quenelle'.
"However, the club cannot ignore the offence that his actions have caused, particularly to the Jewish community, nor the potential damage to the club's reputation.
"The club will make no further comment until the FA's disciplinary process and its own internal investigation have been completed."
West Brom have received negative press since the incident and last month club sponsor Zoopla announced they would not be seeking to renew their deal.