The 34-year-old scored his first Baggies goals with a brace at Upton Park after being recalled to the starting line-up for the first time in over two months.
But during his celebration for his first strike, which levelled the game following Joe Cole's effort for the Hammers, Anelka seemingly performed the 'quenelle' salute made famous by French comedian Dieudonne.
The gesture has been linked to anti-Semitism in his homeland.
After West Brom caretaker manager Keith Downing said Anelka had been "surprised" by the resulting outcry, the player on Saturday night claimed the salute had simply been made as a "special dedication" to his friend.
"This gesture was just a special dedication to my comedian friend Dieudonne," he tweeted in both French and English on his official account.
However, the French minister for sport Valerie Fourneyron had earlier condemned the gesture on Twitter, describing it as "shocking" and "disgusting".
She wrote: "Anelka's gesture is a shocking provocation, disgusting. There's no place for anti-Semitism and incitement to hatred on the football field."
Following the draw, in which Modibo Maiga and Kevin Nolan goals had briefly put West Ham back in front before Saido Berahino finished the goalscoring to earn West Brom a point, interim Baggies boss Downing was quick to defend Anelka.
"I'm aware of it but it has got nothing to do with what is being said," Downing replied when asked about the gesture.
"It is dedicated to a French comedian he knows very, very well. He uses it in his act and I think speculation can be stopped now, it is absolute rubbish really.
"He is totally unaware of what the problems were or the speculation that has been thrown around, he is totally surprised by it."
The FA is aware of the gesture and will be looking into the matter while anti-racism campaigners Kick It Out has offered its assistance to the governing body.
In a statement, Kick It Out said: "Kick It Out has been made aware of West Bromwich Albion striker Nicolas Anelka making an alleged gesture, known as the 'quenelle', which carries antisemitic connotations during today's (28 December) fixture against West Ham United at Upton Park.
"The campaign is in contact with partners in England and France regarding this matter and has offered its support to the Football Association in any forthcoming investigation."
Anelka had not played since the 4-1 defeat to Liverpool on October 26 but was recalled as one of six changes made by Downing, who looked to prevent any tiredness with the game coming less than 48 hours after a Boxing Day draw at Tottenham.
::'Quenelle' means 'scoop' or 'dumpling' and is performed by holding one arm straight by one's side while touching that arm's shoulder with the opposite hand.
::It has been described by its critics as a "Nazi salute in reverse" and, thusly, as an expression of anti-Semitism.
::Forty-seven-year-old M'Bala M'Bala, who goes by the stage name of Dieudonne, has turned the 'quenelle' into something of a viral trend since first performing it four years ago.
::Once a committed anti-racism campaigner, Dieudonne has since been linked to the political far right in France.
::French interior minister Manuel Valls is considering banning all public performances by the comedian. In the wake of Anelka's public use of the gesture, which the player stated was simply a "special dedication" to his good friend Dieudonne, French minister for sport Valerie Fourneyron described his actions as "shocking" and "disgusting".
::Anelka has previously been photographed performing the gesture alongside Dieudonne but Saturday's events brought the debate to England while provoking further outrage and debate in France, where the match was televised.
::Dieudonne, who has past convictions for making anti-Semitic remarks, insists the 'quenelle' is merely "an anti-establishment gesture" but his critics are concerned about its motivation.
::When Dieudonne insulted Jewish radio presenter Patrick Cohen this week, French interior minister Manuel Valls vowed to use any legal means necessary to ban any future public appearances by the comedian. Valls told newspaper Le Parisien: "Dieudonne has been repeatedly condemned for defamation, insult and incitement to racial hatred. He is a repeat offender and I intend to act with the greatest firmness, under the law."
::The English Football Association is considering opening an investigation into the possible connotations of the salute. FIFA rules state: "1. a) Anyone who offends the dignity of a person or group of persons through contemptuous, discriminatory or denigratory words or actions concerning race, colour, language, religion or origin shall be suspended for at least five matches. Furthermore, a stadium ban and a fine of at least CHF 20,000 shall be imposed. If the perpetrator is an official, the fine shall be at least CHF 30,000."