The club reacted swiftly on Thursday following the conclusion of Anelka's independent regulatory commission hearing. The forward was also fined £80,000 for an aggravated breach of Football Association rules and ordered to attend an education programme.
Anelka has the right to appeal and is considering that option.
West Brom said in a statement: "The club has suspended Nicolas Anelka pending the conclusion of the FA's disciplinary process and the club's own internal investigation.
"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 was charged after performing the gesture, which has been described as racist and anti-Semitic, after scoring 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 to be proved.