The injury occurred during a workout Wednesday in Southern California, the team announced. He had an MRI on Thursday morning.
Based on the type of tear, Thompson has been told to expect that he will make a full recovery, a source told ESPN's Adrian Wojnarowski.
Thompson's agent, Greg Lawrence, told ESPN that his client is expected to be fully recovered for the start of the 2021-22 season.
"Klay has a strength of will, but right now it's a tough day for him," Warriors general manager Bob Myers said. "It hurts. He'll get to a place, I think, where he's on the road. But right now, like you or I or anybody, this is a tough day for him to hear that news. It's hard. It's tough."
Myers pointed to a call from an opposing coach and said Thompson is "universally beloved" in the league.
"How your peers feel about you in life I think says more than anything else. And I really believe that," Myers said. "And I think that he is admired within. He's admired without. And you can't put in words what he means to our team, what he means to our fans, our coaching staff, his teammates."
Thompson was playing with several NBA players in Los Angeles and felt pain in the calf area when he landed on his leg, sources told ESPN's Ramona Shelburne.
The 30-year-old Thompson missed all of last season after tearing the ACL in his left knee during Game 6 of the 2019 NBA Finals against the Toronto Raptors. The Warriors were optimistic that Thompson, who has spent more than a year rehabbing the injury, would come back at full strength for the 2020-21 season.
Now they will spend another season without him on the court.
"I can't sit here and say I feel good," Myers said. "I have confidence in our players. I have confidence in our coaches. I have confidence in our ownership. We're going to keep moving. We're never going to stop. But to be truthful, it hurts. It hurts me, and I know it hurts our organization."
ESPN's Nick Friedell contributed to this report.