The procedure was performed to repair a tear in the lateral meniscus of his right knee.
In 17 games this season, Stamkos has 20 points and found the back of the net nine times.
The Lightning (10-6-1) will have to try to continue their good start to the season without their captain who has had his fair share of injury problems over the past couple of years. Last season he missed time due to blood clots, and in 2013-2014 he missed most of the season after breaking his leg.
Tampa Bay is in third place in the Atlantic Division, six points behind the first place Montreal Canadiens.