The European football governing body UEFA said its disciplinary panel found the 24-year-old guilty of "improper conduct" and slapped a €100,000 fine on the striker. However, Bentdner can appeal the decision.
Bentdner, who raised his shirt and lowered his shorts slightly, revealing the name of a betting firm across the top of his underpants, will miss Denmark's opening World Cup qualifier at home against Czech Republic on September 8.
The €100,000 fine imposed on Bentdner is the second-highest by UEFA at Euro 2012. UEFA fined €120,000 on the Russian football association after its fans attacked stadium stewards in Wroclaw following the team's group game against the Czech Republic.
When questioned about the incident involving his underwear, Bentdner said: "It is just a pair of lucky boxer shorts that I used in the first game as well and have used before the tournament. I didn't know I was breaking any rules but I am aware of that now."
UEFA tournament rules bar ambush marketing by unofficial sponsors or advertising on players' kit.
Bendtner was also separately disciplined by the Danish Football Association for flouting team policy. The association has official ties to a rival gambling company.
Denmark were eliminated from Euro 2012 on Sunday after losing 2-1 to Germany.