Foster had complained of the problem on Thursday and on Friday morning had shown no improvement, leading England's medical staff to remove him from Fabio Capello's selection.
Capello has drafted in West Brom's Carson as a replacement, although Joe Hart would have started the Euro 2012 qualfier in any case given he has become the established No. 1 since the World Cup finals.
Carson has won three caps for England, but his only competitive appearance was the ill-fated game against Croatia at Wembley in Euro 2008 qualifying.
He allowed a Niko Kranjcar shot to slip through his grasp as Croatia went on to record a 3-2 win that prevented England from reaching the finals in Austria and Switzerland.
While England's preparations for Saturday's game have been relatively injury free, Wales have been deprived of their best player, Gareth Bale, due to a hamstring injury.