The five wrote in an open letter that they had either experienced, witnessed or heard of abuse of power and sexual harassment by the artistic director of the Tyrolean Festival Erl.
Conductor Gustav Kuhn – who was not named in the letter – founded the festival in 1998 with its summer programme currently taking place in Austria's Tyrol province and is its artistic director.
The women, who worked at the festival between 1998 and 2017, said some of them experienced harassment, such as "unwanted kissing on the mouth or breast, groping under the pullover, a hand between the legs", besides "obscene verbal advances".
The artists – Belarusian violinist Aliona Dargel, German soprano Bettine Kampp, Albanian-Italian violinist Ninela Lamaj, German mezzo-soprano Julia Oesch and Swiss soprano Mona Somm – said they were "outraged" that no action had been taken despite the "widely known facts".
"We were regularly exposed to the unrestrained aggression of the artistic director," they said, adding that mobbing and public humiliation were "daily routine".
"Those who didn't follow the rules were punished with repression and marginalization" which included the withdrawal of roles and contracts, they said.
A spokesperson for Austrian singer Elisabeth Kulman, who helped publish the letter, could not say when exactly the harassment allegedly took place.
Kuhn's lawyer Michael Krueger, a former justice minister, said the director may sue the women over what he called a "manhunt".
A festival spokeswoman declined to comment further. Kuhn is already being investigated over sexual harassment, according to a public prosecution spokesman.
Austrian media said it was the first time that artists had spoken out publicly against harassment in the country.
The claims come amid a worldwide deluge of allegations against powerful men in entertainment, politics and the media.
Accusations of rape and sexual predation by the film tycoon Harvey Weinstein last year sparked the movement dubbed "#MeToo".