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 on Monday confirmed Bendtner will be charged with a violation of the Road Traffic Act and, as a result, will not be considered for international duty for the foreseeable future.
"The DBU has invited Nicklas Bendtner to spend the next six months considering his future as an international," it read.
"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 yesterday 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."
The striker, who has scored 22 goals in 55 matches for Denmark, has now been told by the DBU to use the next six months to think about his international future.
"The DBU has asked the player to carefully consider whether in time he will again be able to live up to the expectations both the Football Association and the public are entitled to have of him as a person and an international," said the statement.
"National team coach Morten Olsen is in agreement with his employers over this decision, which effectively means he will not select Nicklas Bendtner during this period.
"When the coach announces that he will again consider Nicklas Bendtner for the national team, the DBU will initiate talks with the player.
"Should such talks between the the DBU and Nicklas Bendtner lead to a comeback to the national team, the DBU will disclose the details of any conversation."
Bendtner's last international appearance was in a friendly against Turkey last November, and he will now miss a large chunk of Denmark's qualifying campaign for the 2014 World Cup.
I want to know who these clubs are in England where you can (literally) kill someone with your car and get away with it. We sacked our one the minute he was convicted.- Fuzzy_Dunlop