A police spokeswoman told AFP that the graffiti, found on Sunday morning, were being "investigated by the national security agency".
It is the latest in a series of anti-Islamic -- and anti-Semitic -- acts of vandalism in EU member state Austria.
In December unknown culprits left a pig's head and intestines in front of the door of another mosque in the capital. A street sign was changed to read "Sharia Street" in September.
This weekend four swastikas and the word "Hitler" were found drawn and etched on walls on the former Nazi concentration camp Mauthausen.
On Saturday night two men were assaulted in central Vienna by four others shouting anti-Semitic slogans such as "Scheissjuden" ("shitty Jews"), media reports said.
This followed clashes between police and demonstrators protesting against a traditional Viennese ball attended by far-right figures when 54 people were arrested.
Pegida, which has drawn thousands of supporters on the streets of the German city of Dresden in recent months, was due to hold its first march in Austria on Monday evening.
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Small "Patriotic Europeans Against the Islamisation of the Occident" offshoots have also sprung up in other German cities and in European countries including Denmark, Switzerland and Spain.