Inger Stojberg's post was a reaction to the Skovgaard Museum in Viborg's decision not to include the drawing in an exhibition about blasphemy.
"It's the museum's own choice and they have their full right to do it, but I think it's a shame," Stojberg wrote in her Facebook post.
She also adds that the controversial cartoon, which shows an image of a bearded man with a bomb in his turban, is the background screen of her handheld device because it reminds her that Denmark is a country with freedom of speech.
"Honestly, I think we should be proud of the Mohammad cartoons," she wrote.
Last year, Stojberg introduced the "jewelry law" in Denmark mandating that refugees and migrants relinquish their cash and jewelry to pay for accommodation. She was also criticized earlier this year for sharing a picture of herself celebrating the tightening of immigration laws with cake.
The cartoon she posted, considered blasphemous by many Muslims, is the 2005 work of Danish artist Kurt Westergaard.
Westergaard's illustration was one of the 12 caricatures of Mohammad published by the Jyllands-Posten newspaper back in 2006 that caused global riots and three attacks on Danish embassies, resulting in the death of at least 50 people in the Middle East, Africa and Asia.
Since then, the cartoonist has received multiple threats and lives under constant police protection. Eleven years later, another creator of one of the 12 caricatures, Swedish artist Lars Vilks, also lives in fear.