The 36-year-old had trained all week and looked to have recovered from the original injury picked up against Bolton Wanderers in September, but limped off in the first half at Old Trafford on Saturday.
"He'd been doing very well, but it's (hamstring) gone again and maybe we need to give him a longer recovery," manager Sir Alex Ferguson told the club website.
United led 2-0 at half-time against West Brom before a comeback from the visitors levelled scores to leave United third in the league with 14 points from eight games.
Champions Chelsea are five points clear at the top of the table having played the same number of games.
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