Missing half a dozen stalwarts, with six players making their debut and only one joint training session prior to the game, Germany were never going to light any fireworks.
The game, commemorating 25 years since Denmark's 2-0 victory over Germany in the Euro 92 final, saw Germany coach Joachim Loew test several players with an eye on their World Cup defence next year in Russia, but the visitors were lacking their usual high tempo.
Antonio Ruediger's 18th-minute mistake led to the opening goal as he headed the ball into the path of Christian Eriksen who beat Kevin Trapp, making his debut in the German goal, from a tight angle.
Germany gradually worked their way into the game, however, with 29-year-old Sandro Wagner, who netted 11 times in the league for Hoffenheim and who was making his first start, going close on a few occasions as did Leon Goretzka.
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Denmark keeper Frederik Ronnow twice came to their rescue early in the second half but was well beaten when Kimmich turned in the box and scored with a spectacular bicycle kick to rescue a draw.
Germany, who take on San Marino in their World Cup qualifier on Saturday, are top of Group C, five points clear of second placed Northern Ireland.
Denmark, third in Group E and six points off leaders Poland, travel to play Kazakhstan also on Saturday.
(Reporting by Karolos Grohmann; Editing by Toby Davis)
