The 25-year-old, who is currently on loan at Juventus from Arsenal, was stopped by police for driving against the traffic in Copenhagen on Saturday night.
A statement from the DBU: "The DBU has invited Nicklas Bendtner to spend the next six months considering his future as an international.
"The DBU respects any player's right to privacy but also has some rules and expectations regarding the public profile of each player."
Bendtner confirmed his arrest on Sunday on his official Twitter account. He tweeted: "Dear friends i was booked for a mild case of drinkdriving last night it was a quite nite but i am very very sorry to all my friends and fans.
"It is not ok to drink and drive. I take full responsibility."