Harry Kane sent Gareth Southgate's ahead in the 18th minute of the contest, but Denmark levelled the scores courtesy of a stunning strike from Morten Hjulmand in the 34th minute.
The result has left England top of Group C on four points, two points clear of second-placed Denmark and third-placed Slovenia ahead of the final two fixtures in the section.
Despite the disappointment of the result and the performance, Southgate's team are still in a strong position to advance to the knockout round of the competition.
England struggle to make their mark against Denmark
England were unchanged from their clash against Serbia last time out, which meant another start for Trent Alexander-Arnold in central midfield, with Marc Guehi also keeping his spot in the XI after an excellent performance in his first game at a major tournament.
Denmark's side showed one change from their draw against Slovenia, though, and it came in a wing-back position, with Joakim Maehle replacing Alexander Bah.
Manchester United duo Christian Eriksen and Rasmus Hojlund both started, while Barcelona's Andreas Christensen was another notable inclusion for the Danes.
Denmark had a half-chance inside the first 30 seconds, with Pierre-Emile Hojbjerg seeing his effort kept out by England goalkeeper Jordan Pickford after smart work from Hojlund.
Kyle Walker turned an ankle for England in the early exchanges, but he was able to continue, which looked unlikely when replays first showed his foot giving way on the turf, which continued to cut up.
Phil Foden had a half-chance in the 13th minute after working his way into a shooting position inside the Denmark box, but he just lifted his effort over the crossbar.
Denmark well worth a point in Group C contest
The breakthrough came for England in the 18th minute, with Kane sliding the ball into the bottom corner from close range after a horror mistake from Victor Kristiansen, who allowed Walker to break into the Denmark box, and the ball eventually came for Kane, with the Bayern forward, as expected, taking the chance.
Denmark enjoyed a strong spell in the period that followed, with Hojlund just unable to sort out his feet in time inside the England box after a clever flick from his club and international teammate Eriksen.
The Danes levelled the scores in the 34th minute of the contest, and it was a stunning hit from Morten Hjulmand, with the midfielder, who is believed to be of interest to Manchester United, finding the bottom corner with an effort off the inside of the post.
Denmark were dominant, with Morten Hjulmand having another one deflected wide of the target late in the first period, before Joachim Andersen headed over the crossbar and Hojbjerg tested Pickford, and Kasper Hjulmand's side more than deserved to be level at the half-time interval.
England would have been looking for a fast start in the second period, but that was not to be, with Denmark certainly looking the more productive outfit.
Bukayo Saka headed into the side-netting after beating Kasper Schmeichel to a bouncing ball, while the Denmark goalkeeper was also needed to keep out a strike from Declan Rice.
England made to wait for Euro 2024 last-16 qualification
Foden then struck one off the post, with England looking the more dangerous, and it was Denmark's turn to sit back as the match approached its final 30 minutes of action.
Schmeichel had to be at his best to deny Ollie Watkins in the 72nd minute, with the Aston Villa striker entering the field alongside Jarrod Bowen and Eberechi Eze, which led to Kane, Foden and Saka all departing after finding it difficult to make their mark for long spells.
Pickford was then called into action to deny Hojbjerg down the other end, with the Tottenham Hotspur midfielder putting in a strong performance in Frankfurt.
Andreas Christensen headed one over the crossbar for Denmark late on, before Hojbjerg hit one just wide, with England's goal coming under attack in the latter stages of the contest, but neither team could score a second, as the points were shared on Thursday night.
When are Denmark, England next in action?
England will conclude their Group C campaign against Slovenia on Tuesday, while Denmark will take Serbia on the same night, with all four teams still capable of advancing to the round of 16.