The defender was forced off late on in the Premier League defeat at Southampton on Saturday evening amid concerns he may have suffered cruciate knee ligament damage.
However, West Brom said scans had revealed the problem is not as serious as initially feared and the 27-year-old will not need an operation.
"The injury gave Craig a serious thigh muscle bleed and a torn knee capsule," said Dr Mark Gillett, the club's director of performance.
"It's a serious injury, but we are heartened that it's already showing an improvement and surgery is not required."
Dawson has played at right-back and centre-half this season, starting all 11 of West Brom's matches in all competitions.
Source : PA
Source: PA