Bendtner, who lifted his shirt to show the name of an Irish firm on his waistband after scoring his second goal in the 3-2 Group B loss to Portugal on Wednesday, will be suspended for the opening match of Denmark's 2014 World Cup qualifying campaign.
The 24-year-old Arsenal forward can lodge an appeal within three days.
The Danes were eliminated from Euro 2012 after losing 2-1 to Germany on Sunday.
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