The 23-year-old played a part in all three of the Red Rose's victories over Australia in June, but will now miss the start of his club side's Aviva Premiership season.
Nowell went under the knife a fortnight ago and is now likely to sit out matches against Wasps and defending champions Saracens in the coming weeks.
"Jack Nowell is out after an operation on an injured thumb so he is going to be out for a while," head coach Rob Baxter told the club's official website.
"It is potentially something like an eight-to-10 week injury. Other than him, though, we are looking pretty good and have a pretty good squad for the start of the season."
Nowell has gone on to become a regular for England at senior level since breaking through the Under-20s side, making him a contender for next year's British and Irish Lions side.