Denmark have been also fined $81, 600 and ordered to play their next four home games at least 250 km away from Copenhagen, the European governing body announced on Friday.
They will also have to play their next Euro qualifier against Liechtenstein on September 12th behind closed doors.
Denmark made a magnificent comeback from three goals down to level the score to 3-3, but the entertaining display was overshadowed by a late fracas.
It started when Denmark midfielder Christian Poulsen struck Markus Rosenberg inside the area, and German referee Herbert Fandel had no option but to send the Sevilla midfielder off and award an 89th-minute penalty.
As soon as the referee took action, an angry fan stormed in rage towards him, but he was bravely blocked by Denmark defender Michael Gravgaard.
Poulsen has been banned for three international matches as a result of his improper action.