Slade picked up the injury during the Six Nations earlier this year and it worsened during England's matches in Japan and New Zealand last month, Baxter said.
Slade had the surgery earlier this week.
"It’s a relatively complex operation which, at this stage, makes it a little difficult to talk about his return to play time," Baxter said in a statement.
"It is likely to be in the three-to-four-month range so unfortunately, he is going to miss a good chunk of the start of the season with us."
Exeter, where Slade has played since 2012, begin their Premiership Rugby campaign on September 21st against Leicester Tigers.
Slade, who has earned 65 international caps and scored eight tries, will be in a race to get fit for England's November fixtures against New Zealand, Australia, South Africa and Japan.
"He will return very fit, as he’s been on great form for club and country," Baxter added. "I predict he will still have a very big impact on next season both for us and for England."
