The Frenchman joined the club during the close-season on a one-year deal from Chinese outfit Shanghai Shenhua, and had a productive pre-season campaign for the club.
He made his competitive bow for the team in Saturday's 1-0 defeat to Southampton at The Hawthorns, but the club did not confirm when they expect him to return to action.
A statement on the club's website read: "West Bromwich Albion can confirm that Nicolas Anelka will not be involved in Saturday's game at Everton.
"The club have excused the striker from club duty on compassionate grounds."
Anelka has had a much-travelled career, with West Brom becoming the sixth Premier League team he has featured for.
He previously won Premier League titles with Arsenal and Chelsea and won the Premier League golden boot in the 2008-09 season.
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