France's sports minister accused him of a "disgusting anti-Semitic" gesture.
Anelka meant no offence - Downing
A statement from West Brom said: "The club has asked Nicolas not to perform the gesture again. Nicolas immediately agreed to adhere to this request."
The French government is trying to ban comedian Dieudonne M'bala M'bala's shows over his use of the gesture and Anelka confirmed
he did it in support of the performer.
But West Brom instructed Anelka not to use the gesture again after acknowledging "the goal celebration has caused offence in some quarters".
The club will continue to consider the Frenchman for matches while the matter is being investigated internally and by the Football Association.
"Nicolas was asked to explain his goal celebration by caretaker head coach Keith Downing within minutes of the game finishing at West Ham," the statement read.
"Nicolas said that he performed the gesture to dedicate his goal to a friend and vehemently denied having any intention to cause offence.
"Upon reporting for training this morning, Nicolas was asked by sporting & technical director Richard Garlick to give a full explanation about his goal celebration, during which he again strongly denied intending to cause offence."
West Brom have told the FA they will help with their enquiry as well as holding their own investigation, a process which they say "will remain confidential between the club and Nicolas".
Caretaker boss Downing confirmed that "football reasons" alone would determine whether Anelka plays against Newcastle on New Year's Day, although he will assess the player's mindset before selecting him.
"I will have to have a chat with Nicolas and make sure his mind is clear," Downing said. "He's obviously on the back of two goals and I am sure he will want to play."
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