Anelka, 34, made the sign - described as an inverted Nazi salute - after scoring his first of two goals in Saturday's 3-3 draw at West Ham.
France's sports minister accused him of a "disgusting anti-Semitic" gesture.
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 on Twitter 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."
But what is the 'Quenelle' gesture, which has caused upset in France but went almost unnoticed by the average English supporter?
The gesture involves touching or gripping your shoulder with one hand while holding the palm of your other hand outstretched and pointing to the ground. Some describe it as a combination of the bras d'honneur with a bent arm (which means "up yours") and the Nazi salute.
It is the trademark of the hugely controversial French comedian Dieudonne M'Bala M'Bala, who once said he would like to put a quenelle - a rugby-ball-shaped serving of fish or meat paste - up the backside of Zionists.
Dieudonne made the gesture when he headed his own anti-Zionist campaign in the European elections in 2009. French media trace it further back, to one of his performances in 2005. It came to greater prominence in September when two soldiers were photographed appearing to make the gesture outside a Paris synagogue.