Ahmet Demir, a politician in Tyrol with the Green party, has since taken the post down and apologised if he offended anyone but defended his post.
In a second message posted on Facebook he explained that he was trying to convey that “every woman should be able to wear what they want as long as they chose the clothes themselves”.
His original post came after some French beaches adopted a controversial burqini ban and after comments made by Austrian cabinet politicians criticising the full face veil.
Demir received a mixed response to the original post and photo, with some commentators supporting his point and others criticising him for being “against” nuns.
One politician said his comparison of a burqa, a full veil covering that is sometimes worn by Muslim woman, with a nun's habit in “inappropriate”.
“Full veils have never had a place in our society,” Reinhold Lopatka, from the right-wing OeVP party told the Tiroler Tageszeitung. “Niqab and burqa stand for intolerance and oppression of women, habits are symbols of a spiritual life in a freely chosen community.”
However, like nuns, many Muslim women argue that they choose to wear the full face veil voluntarily.
Speaking to the Oesterreich newspaper recently, Austria's Foreign Minister Sebastian Kurz said he believed the burqa is “a hindrance for integration”.
Interior Minister Wolfgang Sobotka also said he can imagine banning burqas for “car driving, on entry, or at demonstrations”, although he is against a full ban on face veils.
The presidential candidate for the far-right Freedom Party, Norbert Hofer, has said a burqa ban would be “useful”.