Bale has enjoyed a fantastic season with Tottenham Hotspur, particularly in the Champions League where he scored a hat-trick against Inter Milan in the San Siro.
He returned to action two weeks ago following a six-week layoff with a back problem but has now suffered a hamstring strain that rules him out of the 100th meeting between the two countries.
"He felt tight last week during training with his club," the Football Association of Wales said on their website.
"After playing 90 minutes on Saturday he felt some muscle tightness. Initially, this was expected to be muscle soreness after playing his first game.
"On joining-up with the Welsh squad he was kept off his feet in training for two days to recover. As he still felt tight in the warm-up on Tuesday, Gareth was pulled out of the session.
"He did not train at all on Wednesday and was sent for a scan which revealed that he had picked up his injury last week."
Wales have lost all three of their Group G games while England are second in the standings with seven points from three games.
Montenegro are the surprise pacesetters with 10 points from four games.
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