Bendtner's financial penalty is the second highest imposed by UEFA at Euro 2012. The Russian football association was fined 120,000 euros after its fans attacked stadium stewards in Wroclaw following the team's group game against the Czech Republic.
Bendtner raised his shirt and lowered the top of his shorts slightly, revealing the name of a betting firm across the top of his underpants, after scoring his second goal in a 3-2 loss against Portugal last Wednesday.
The laws of football managed by FIFA relating to players' equipment also state that players "must not reveal undergarments showing slogans or advertising."
UEFA tournament rules also bar ambush marketing by unofficial sponsors or advertising on players' kit. European Championship matches typically get average worldwide ratings of 150 million television viewers, who are counted if they watch at least 30 minutes of a game.
The Irish gambling firm Paddy Power, which based a marketing campaign around the "lucky pants" later worn by Bendtner, said it would support his appeal.
"This is a hysterical and deeply cynical move by UEFA dictated by pure commercialism and is a far greater penalty than recent UEFA fines for far more serious incidents," the company said in a statement on its website.
At Euro 2008, UEFA fined the Croatian football association 20,000 Swiss francs for fans "displaying a racist banner and showing racist conduct" toward Turkish fans during a quarterfinal match.
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 was eliminated from Euro 2012 after losing to Germany 2-1.
- AP