Club captain Martin featured 35 times in all competitions last season as Norwich slumped to relegation back to the Championship after a three-year stint in the Premier League.
Martin went under the knife at the end of 2013-14, but Adams does not expect the procedure to hamper his ability to return for pre-season training at the end of the month.
"Russell has just had a little hernia operation," he told the club's official website.
"He wasn't in too much pain, but we decided to do it really early and you're talking two weeks after the operation now, so he's got plenty of time.
"He's back on the treadmills so it's no problem at all for him."
Adams also revealed that the medical team at Norwich have yet to decide on the best course of action for Martin Olsson, who struggled with a minor shoulder problem last term.
"He played through the season with it and it wasn't an absolutely essential operation," Adams added.
"It's one to sit down with the physios and decide, because that would be a longer term one.
"As we saw through the season he had problems with it, but he could pop it back in and he was ready to go again."