Wijnaldum limped off after 15 minutes at Anfield, having seemingly suffered the injury in an innocuous challenge, with club captain Jordan Henderson replacing him.
Liverpool moved a point clear at the top of Group E after second-half goals from Mohamed Salah, Emre Can and substitute Daniel Sturridge, although James Milner had a penalty well saved by veteran Maribor goalkeeper Jasmin Handanovic.
But, with Philippe Coutinho already on the sidelines, victory over the Slovenian champions came at a cost for Liverpool and Klopp.
"Nobody spoke to me so far [about it]," Klopp told a news conference. "At half-time I asked immediately and the ankle was already swollen. It's probably not a good sign.
"We saw a kick in the game and didn't think it was too serious. Then it was swollen. We're not sure if he twisted it or not. For sure, we have to make a scan."
Coutinho missed the Maribor game with an adductor injury and Klopp does not expect the Brazilian playmaker to be fit for Saturday's Premier League game at West Ham, although defender Dejan Lovren may be available if he can shake off a thigh problem.
"I would say it will be really close," Klopp said. "I don't think Phil is able to play, but with Dejan we have to see.
"It is different with Dejan. It's not the same problem Phil has and he is not out for that long a time, but Gini is out so maybe there will be a wonder or something like this and Phil is in.
"But I don't think in the moment that he can play."
But Klopp has a headache with Liverpool failing to convert a penalty for the second time in two games, Salah having been denied in the Premier League victory against Huddersfield Town at the weekend.
"It was a good penalty and a fantastic save," Klopp added. "We have to think about it.
"I know these boys usually do it from 12 yards but we will find a solution."