The woman died after being shot late on Thursday in a northern district of the capital Vienna, prompting the interior ministry to announce a summit next week to discuss ways of addressing the spate of killings of women by their ex-partners.
Police confirmed to AFP that a 42-year-old man had been arrested on suspicion of committing the murder with a handgun.
According to Austrian media, the suspect in the latest murder is a man who hit headlines in 2018 when a Green politician Sigrid Maurer accused him of sending her obscene Facebook messages.
Maurer said she had gone public with the case in order to draw attention to the problem of online harassment.
The man denied writing the messages, saying they had been written by someone else from a computer used by customers at the bar he runs and sued Maurer for defamation.
A court ruling backed him, saying that Maurer should have taken more care to establish whether he really did write the messages.
But the man later dropped the complaint, with Maurer being exonerated.
The case drew much attention in Austria with the initial decision against Maurer being condemned by feminist activists and others.
On Friday, Maurer said that “the fact that it seems the culprit was the bar owner is personally shocking to me”.
Women’s Minister Susanne Raab was one of many other politicians to react to Thursday’s “shocking murder”, saying she was “profoundly saddened”.
Green Transport Minister Leonore Gewessler was visibly moved as she called for more action on the issue at a press conference.
Austrian media have been raising the alarm over high levels of femicide, with 31 killings of women in 2020.
One of the country’s most important news weeklies, Profil, devoted an issue to the subject recently and cited Eurostat figures showing that Austria was the only country in which more women than men were victims of violent crime.