Goals from Christian Poulsen and Thomas Enevoldsen gave the Danes victory in Aalborg the day before their departure to South Africa for the June 11-July 11 tournament.
Head coach Morten Olsen used the game to try out his options before he names his final 23-man squad on Friday and the injury to regular starter Kjaer late in the game will have worried him.
"He has had an impact on the side of the ligament, a knee injury," team doctor Soren Kaalund was quoted as saying by local news agency Ritzau.
"He seems stable and we are reasonably confident but if there is major damage then it's something that takes a long time.
"We will evaluate it and he will have a scan."
IFK Gothenburg goalkeeper Kim Christensen made his international debut before being replaced by Jesper Christiansen of FC Copenhagen at halftime. Only one of them will join fellow keepers Thomas Sorensen and Stephan Andersen in the final squad.
Simon Poulsen and Patrick Mtigila got 45 minutes each at left back to impress the coach, with Poulsen making a good attacking contribution in the first half.
It looked like striker Jon Dahl Tomasson had finally equalled Poul Nielsen's record of 52 international goals for Denmark with an acrobatic first-half effort, only for midfielder Poulsen to get a final touch before the ball crossed the line.
Enevoldsen then struck in second-half stoppage time to make it 2-0.
Neither forward Nicklas Bendtner nor Sorensen took part as they continue to recover from groin and elbow injuries respectively, while midfielder Daniel Jensen missed the game as a precaution having pulled up in training on Wednesday.
The Danes take on Netherlands in their opening game in Group E in Johannesburg on June 14. Japan and Cameroon are the other teams in the group.
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