The Gloucester wing or full-back, who made his Test debut during England's tour of Argentina earlier this summer, suffered an elbow injury during a pre-season game against European champions Toulon at Stade Felix Mayol on Friday night.
May's fellow wing Shane Monahan (shoulder) was also injured in the match.
"We will just have to wait and see what kind of timescale we're looking at for both," Gloucester rugby director Nigel Davies told the club's official website.
"They will be assessed further this week and we will take it forward from there.
"But I think it is fair to say neither injury will be short term. It is disappointing to pick up injuries, especially at this stage of proceedings.
"They have both looked sharp in training, and they showed up well out there on Friday, so it's hugely frustrating for them after working so hard in the pre-season up to this point and being ready to get going in matches."
Gloucester, who were beaten 42-17 by Toulon, kick off the Premiership season against Sale Sharks at Kingsholm on September 7.