In the night between Saturday and Sunday, the man broke into the Lauder Chabad school and smashed the windows, glass cabinets and sanitary ware on the school's three floors.
The police disclosed only the perpetrator's initials, saying that he had a Croatian passport, was born in Virovitica and had permanent residence in Zagreb.
The police are investigating the circumstances and motives of the attack.
The Austrian media today reported about the attack, which the Jewish community in Vienna condemned as an act of vandalism and the gravest anti-Semitic incident in Austria in the last 20 years.
Ephraim Zuroff, head of the central office of the Simon Wiesenthal Centre in Israel, told the Jerusalem Post today that he was not surprised that the incident had occurred in a country that protected Croatian Nazi war criminals.
Zuroff was referring to the case of Milivoj Asner, who he said was a Croatian Nazi war criminal living in Klagenfurt. Croatian authorities have been demanding his extradition for more than a year so that he could be put on trial for his role as police chief in Pozega in 1941 and 1942.
Austria is refusing to extradite Asner despite the fact that he is not an Austrian national and that there is no reason whatsoever not to comply with Croatia's request, Zuroff said.
He also stated that Austria had failed to successfully prosecute Nazi war criminals for more than 30 years and that such an atmosphere of impunity enabled incidents like the latest one.