Wallace, 28, has featured in all of the Clarets' four fixtures to date but discovered surgery was necessary after a scan.
Boss Sean Dyche will be without Wallace for several months and he said: "It's unfortunate for Ross. He came back from pre-season flying and we didn't expect any problem.
"He did have a niggly knee last season, but we felt we were on top of it and so did he, but it has just gathered a little bit of pace and got too sore to continue, so it's about time he had something done about it.
"He needs an operation and the specialist will know more once Ross gets in hospital, but we have had a scan and there are some details that need tightening up.
"But it's certainly going to be weeks and could be a few months and we believe it will take care of itself once he has had surgery.
"The body takes a lot of hammer playing football and there is nothing we can do really.
"It's part of the body's make-up. Footballers do put the body through a lot of stress and over time there's wear and tear.
"But Ross needs this sorting out and we felt it was appropriate to get it sorted straight away."