The advice by Vienna police boss Gerhard Pürstl came as it was revealed that several women in Salzburg reported being sexually assaulted by men on New Year's Eve.
Three men have since been arrested, with police saying in a statement that they are Syrian and Afghan nationals.
In neighbouring Germany, more than 100 women have come forward to say they were assaulted over New Year by groups of men who were reportedly of Arab or north African appearance.
In the wake of the German scandal, Pürstl was asked about the incidents and about the risks that women face. "Women should in general not go out on the streets at night alone, they should avoid suspicious looking areas and also when in pubs and clubs should only accept drinks from people they know," he told the Krone newspaper.
The statement immediately attracted criticism from Green party women's affairs spokesman Berivan Aslan who said: "Should women now only go out with bodyguards if they want to avoid being told it was their fault when they get into difficulties?"
And the Green party security spokesman Peter Pilz said: "Is the Vienna police chief saying that he is no longer in a position to protect women from sex attacks? If so, then he has failed in his job."
The Vienna SPÖ's Women's Affairs spokesman, Sandra Frauenberger, added: "The first reaction to incidents like this should not be to tell women to be more careful. The proper reaction is for us all to work together to fight problems like this."
Austria's Interior Ministry Johanna Mikl-Leitner also waded into the debate saying: "The police will make sure that they tackle every sex assault case with zero tolerance. We women will not allow ourselves to see our freedom to go where we want, when we want, reduced by even a millimetre".
Pürstl meanwhile defended his statement, saying he was simply repeating advice that had been given out by police for decades as part of a general crime prevention strategy. He said it was the same message that was repeated after a spate of cases where women were tricked by strangers into accepting spiked drinks.
The police are already under fire in Austria after admitting only revealing the incidents of sex attacks in the city of Salzburg when the full extent of the German problem had become known. A police spokeswoman has said it was nothing to do with a conspiracy of silence, and that they had acted out of respect for the victims.
So far police said there had been ten cases in which women had come forward to complain.
Story courtesy of Central European News.