The England and Lions No.9 strained a thigh muscle in Saturday's victory over Leeds Tykes and had to be replaced early on in the second half.
With Dawson likely to be sidelined for three weeks, the 30-year-old may be fit for the Zurich Premiership Final which takes place on May 31 – if his side can beat in-form Wasps in the semi.
This is just the latest in a series of injuries suffered by Dawson during the past 12 months. As well as a lay-off between December 2002 and January 2003, the scrum-half underwent surgery on his knee during the off-season.
Northampton Saints pulled off a final-day coup by sneaking into the Zurich Premiership play-offs, their 28-6 win over Leeds at Franklin's Gardens, and Sharks' failure to get a point at Saracens, meaning that the Saints finished the season in third place, giving them a shot at the title.