Of the 15-member EU, only Denmark, Sweden and the UK opted not to adopt the euro when it was launched in January 1999.
Denmark will hold a referendum on whether to join the European Monetary Union and adopt the European Union's single currency in September.
The critically-acclaimed director of Breaking The Waves, The Idiots and Bjork vehicle Dancer in the Dark, wants Danes to vote "yes".
Von Trier and his film company, Zentropa, have dropped their fees for the film, which is being made for the pro-European Danish party Centrum Demokraterne.
Euro-sceptic
"Trier and I find it important that Denmark's cultural scene participates in the euro debate," Zentropa chief Peter Aalbaek said on Monday.
Of the 15-member EU, only Denmark, Sweden and the UK opted not to adopt the euro when it was launched in January 1999.
Euro-scepticism is strong in Denmark with recent opinion polls showing more Danes against the common currency then in favour of it.
Von Trier's film will counter resistance by explaining that Danish euro currency will continue to bear a portrait of the Danish monarch, Queen Margrethe.
Controversy
Lars von Trier is no stranger to controversy. The Idiots offended censors by including an orgy scene.
A signatory to the strict Dogma principles of no-frills film-making, von Trier reportedly bullied Björk into her performance in Dancing in the Dark.
But his methods paid off and the film won the top Palme d'Or prize at the Cannes film festival. Björk won the best actress award.