Bendtner, on a season-long loan to Juventus from Arsenal, was stopped by police after driving against traffic in downtown Copenhagen late on Saturday night. An alcohol test showed he was well over the legal limit.
The Danish Football Association decided on Monday to ban the 25-year-old forward for six months and urged him to use the time to reflect on his behaviour.
"The DBU (Danish FA) are then happy to have dialogue with him about how he in the future see himself contribute positively to the men's first squad," it said in a statement.
Bendtner himself, currently out injured, was quick to express remorse and take responsibility on Twitter, later issuing a release promising to come back as quickly as possible.
"This is the worst thing that can happen to a footballer. However, I would like to emphasise that I fully respect DBU's decision, and that I will work hard to get back to the national team, which I love, as soon as possible," he said.
"I am deeply sorry for my misjudgement Saturday night, and I accept full responsibility."
This is not the first time Bendtner has been in trouble for his off-field behaviour. In 2011, while on loan at Sunderland, he was arrested but later cleared of vandalising cars in Newcastle.