The drawing posted by Sara Mats Azmeh Rasmussen shows a bearded man standing next to three people, including two women who are almost entirely veiled, with the caption: "If you do not like to be drawn, cover yourself, Prophet."
The writer, who describes herself as "an author and human rights activist with a Muslim background", said on her blog that she wanted to show her solidarity with satirical French weekly Charlie Hebdo, which last month stoked controversy by publishing cartoons showing the prophet naked.
The French newspaper's cartoon added to anger in the Muslim world, where often violent protests erupted last month over a crudely-made American anti-Islam film "The Innocence of Muslims".
"It is not only necessary to explain and defend freedom of speech and expression, but there is definitely a need for even more cartoons of the Islamic Prophet drawn by Muslims, so the point becomes clearer: it is not a conflict between East and West or Muslims and Christians," Rasmussen wrote.
"It is rather a conflict between dogma and democratic spirit and culture. This conflict exists inside the Islamic world."
A staunch supporter of gay rights, Rasmussen previously hit the headlines in 2009 when she burnt a hijab in public on International Women's Day.