Bendtner was not in the squad for Arsenal's 1-1 Champions League draw at Bayern Munich on Tuesday which sent them out of the competition and media reported on Thursday about an alleged altercation with a taxi driver.
An unnamed taxi driver told Danish newspaper BT that after asking Bendtner to leave his cab, the striker then pulled down his pants, started rubbing his abdomen against the cab window, while shouting "I will f*** you" and whipping the car with his belt.
Wenger told a press conference on Friday: "I don't know what happened. The only thing that is for sure, nobody gave him any permission to go to Copenhagen.
"He will be fined for that.... his contract ends at the end of the season."
The 26-year-old forward, who appeared for the Danes in their 1-0 loss to England at Wembley two weeks ago, is expected to leave Arsenal at the end of the season, ending a turbulent time at the Premier League club he joined in 2005 from FC Copenhagen.
Bendtner struggled to secure a place in the team and spent much of his time on loan at Birmingham City, Sunderland and Juventus.
Bendtner, who has played 58 times for Denmark and scored 24 goals, was suspended by the national team for six months following a conviction for drink driving in March 2013.
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