Mawson was pulled out of the warmup in the FA Cup game against Sheffield Wednesday. There were fears of a serious injury.
However, scans have showed that there is no serious damage. He will be managed during the last few weeks of the season, and then the club will make a determination about whether surgery or further treatment is needed.
"After seeing a specialist and undergoing an MRI scan, the influential defender is set to rejoin his team-mates on the training ground ahead of the Brighton clash," said a club statement.
Swansea are currently out of the drop zone, but they are aware that even a couple of bad losses could see them dragged back into the bottom three.