The midfielder, who can also play at full back, is suffering from a back problem that has derailed his season so far.
Garner has been dealing with back problems during his career, but this is said to be unrelated to the one he experienced in 2022-2023.
Manager Sean Dyche stated: "Jimmy Garner is very unfortunate.
"He's got a longer-term injury. I mentioned last week about getting assessment from the specialist and they've advised to slow him down again, take him off the grass.
"So we're going to have to wait and see on that one, but it's going to be weeks. It's not going to be days, that's for sure.
"It's a back injury they have just got to be a bit careful with. It's not connected to his previous one, it's just one of those things.
"But it will be a longer period, not a short one. Beyond another month, I would think."