The attacker picked up an ankle injury in a 2-1 loss to Manchester City at the weekend.
Wissa, who has been in fine form so far this term, will now miss a chunk of game time.
Post-game, boss Thomas Frank stated: "Wissa is, unfortunately, not good news: it looks like an injury that will be a couple of months.
"It’s very frustrating. We talked about our many injuries last year, I hope I don't have to talk too much about it this year, I maybe already have.
"We were unlucky with Igor Thiago), unlucky with (Aaron) Hickey; we've then had two contact injuries with Mathias Jensen and Yoane Wissa, so that's very frustrating.
"But that's part of football, we move on, and we will find solutions."
He added: "It will leave a big hole. Everybody was saying we bought Igor Thiago to replace Ivan (Toney) - but we still had Wissa; we bought Igor Thiago to build the squad and provide competition in the squad.
"Wissa had a very good season last year and I thought he has started the season very well this year, with three goals in four games, that's a very good number.
"He's just been very important for us and that's going to leave a hole. But, again, I will find a solution."