Soren Svenningsen, 47, who owned the now disbanded Team Capinordic cycling team, was found to have traces of three banned substances following the race.
"On June 30, veteran cyclist Soren Svenningsen tested positive in a doping test in a Danish H40 race. The sample showed traces of two different glucocorticoids and testosterone," the statement said, adding that Svenningsen would leave the board and his position as chair of Holte Cycling Club with immediate effect.
"I am deeply shocked to have received the news of Soren Svenningsen's positive drug tests. We stand for a clear and consistent doping position in the DCU," the statement quoted union president Tom Lund as saying.
"That a leader in Danish cycling who is also a board member of DCU tested positive, and thus breaks our trust, is inexcusable.
"As president of DCU, I would like to emphasise that our anti-doping line will continue to be sharp and consistent, and we will continue to hunt down cheats," said Lund, adding that testing was necessary in the veteran classes to weed out the doping problems that have plagued cycling for decades.