The 25-year-old, who is currently on loan at Juventus from Arsenal, was stopped by police on Saturday night after he was spotted driving against the traffic in the city centre.
Bendtner appeared in court on Tuesday in the Danish capital, where he was handed a fine and a driving ban after pleading guilty.
"I can honestly say this is the worst day of my life," he told newspaper Ekstra Bladet afterwards.
"I can't describe how much pain I'm going through at this time."
Bendtner had confirmed his arrest on his official Twitter account on Sunday, saying: "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."
His actions have also cost him a place in the Denmark squad for the foreseeable future, with the Danish FA (DBU) announcing on Monday he will not be considered for selection for the next six months.