The Birmingham City keeper, understudy to first-choice stopper Joe Hart of Manchester City, will be replaced in the squad by West Bromwich Albion's Scott Carson for Saturday's Group G match in Cardiff.
"Ben Foster has returned home this morning with a throat infection," the FA said on its website.
England are second in the group with seven points having played one game fewer than leaders Montenegro (10). Wales are bottom with no points. The other teams in the group are Switzerland and Bulgaria.
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