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."
SUNDERLAND FIXTURES
March 2013
Sat 09 15:00 A Queens Park Rangers
Sun 17 13:30 H Norwich City
Sat 30 12:45 H Manchester United
April 2013
Sat 06 15:00 A Chelsea
Sat 13 13:30 A Newcastle United
Sat 20 15:00 H Everton
Sat 27 15:00 A Aston Villa
May 2013
Sat 04 15:00 H Stoke City
Sun 12 15:00 H Southampton
Sun 19 16:00 A Tottenham Hotspur