The 32-year-old, who has been with the club since 2008, will be sidelined for "at least four months" as he recovers from the problem.
"Whenever you talk about big toe injuries they sound relatively minor, but they can be pretty complex," Baxter told BBC Sport. "When it involves the bottom of the foot and the ligaments around the toe, as it does with Matt, it could be a relatively long-term injury.
"He's a real good leader of the culture we have here and the quality of people we want around, so it is a shame for him not to be available, but he will very quickly be able to be involved in and around the club in other roles and other ways.
"Matt is also coming to the age where he is starting to consider his next career options and what this allows him to do while he is rehabilitating is to think about some of those things as well - ideally we'd like him to stay around the club."