The Freedom Party, which has previously called for the Quran to be banned, said the contest had been approved by the country’s counter-terrorism agency.
Drawings will be judged by American cartoonist Bosch Fawstin, winner of a similar competition in Texas three years ago that was targeted by two Muslim gunmen.
Many Muslims consider images of Prophet Muhammad to be blasphemous and cartoons depicting him have previously provoked violent responses.
“Freedom of speech is threatened, especially for Islam critics,” Mr Wilders said. “We should never accept that. Freedom of speech is our most important freedom.”
The far-right MP claims Islam is a totalitarian political ideology rather than a religion. He has previously called for mosques and Islamic schools to the shut down and for a blanket ban on Muslim immigrants.
In 2016 he was convicted of inciting hatred and discrimination after asking supporters whether they wanted “fewer or more Moroccans” in their country.
When the crowd shouted back “fewer”, a smiling Mr Wilders answered: “Then we’ll fix it.”
On Saturday the MP spoke in London to crowds of Tommy Robinson supporters, who were protesting the English Defence League founder’s jail sentence for contempt of court.
The Freedom Party, which is the leading opposition party in the Netherlands after coming second in elections last March, said the cartoon competition would be held in the autumn after getting the go-ahead from the NCTV counter-terrorism agency.
The party is offering a €5,000 (£4,000) prize for the winner.
“Muslims can be offended to death. That’s not the problem,” tweeted Mr Fawstin, who is publishing a book of cartoons of the prophet. “Muslims MURDERING over cartoons is the problem. And that has to be defied by drawing Mohammad.”
Two gunmen from Arizona were shot dead by police as they tried to storm the 2015 competition won by the cartoonist in Garland, Texas.
That contest was held four months after Islamist gunmen murdered 12 people at the Paris offices of the French satirical newspaper Charlie Hebdo, which had printed cartoons of the Prophet Muhammad.
In 2005, the Danish newspaper Jyllands-Posten provoked protests across the world and riots in some Muslim countries by publishing several cartoons of Muhammad, including one depicting the prophet with a bomb in his turban.
The newspaper's editor had invited submissions from illustrators in what he described as an examination of Islam and self-censorship.
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