Owen was forced off after 66 minutes of Tuesday's 1-0 home defeat to Dagenham with suspected ligament damage, although the club are awaiting the results of an X-ray before they can fully diagnose the problem.
Vale physio John Bower told The Sentinel: "We think Gareth has suffered ligament damage, it's just a question of finding out the extent of the damage.
"We will see how the injury settles down over the next 48 hours. It has settled down quite well up to now and it isn't as bad as we thought. The X-ray will reveal if he has suffered a fracture. If he hasn't he might have an MRI scan, probably early next week, to find out if there is any soft tissue or ligament damage.
"He is likely to be out for four to six weeks if it is ligament damage, which means he will only return for the last two or three games of the season."
The news will come as a major blow to manager Dean Glover, who is already sweating on the fitness of fellow defender Lee Collins (hip) ahead of this weekend's clash against Darlington.