May was experiencing discomfort in his knee over the holiday period and went under the knife to remove a cyst below his knee.
The club is not expecting it to affect his preparation for this season.
“Maysie had a cyst pressing on the nerve of his knee which required some treatment,” Demons high-performance manager Darren Burgess told the club website.
“His pre-season has been outstanding so far and this won’t affect his program going forward.”
Meanwhile, Smith had an infection in his foot after cutting it on a sharp object at the beach.
“Joel cut his foot while on holidays which was pretty unlucky,” Burgess said.
“He treated it straight away and did all the right things, but that wound got a bit infected, so he’s just had to look after it.”
The pair are expected to resume running next week in the rehab group.