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."
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.
