The memorial is located in a park close to Salzburg's famous Mirabell Palace, which also houses the city government.
City officials believe it was attacked with some force - possibly with a pickaxe. They expect to raise around €3,000 from a fundraiser among Salzburg’s municipal councils and the city government has said it will double what they raise.
Recently there have been a spate of what are thought to be acts of right-wing vandalism in Salzburg. In early May several Stolperstein - cobblestone-sized memorials for individual victims of Nazism - were defaced.
The synagogue and the Jewish community have also been the target of attacks, as well as an anti-fascist memorial in Salzburg's cemetery. The Caritas emergency shelter, which sometimes gives refuge to beggars from Romania, was smeared with Nazi slogans.
The euthanasia memorial was built in 1991, in remembrance of 500 sick and disabled people who were deported by the Nazis from a state hospital to Hartheim Castle near Linz, where they were murdered as part of 'Aktion T4' - the Nazi euthanasia programme.
The memorial is a glass rectangle holding a bed of sand and ash to symbolise the Nazi's victims. It is hoped it can be repaired by mid-July.
A €10,000 reward has also been offered to anyone who has information about vandalism that occurred at the Mauthausen concentration camp in May.
Mauthausen Committee chairman Willi Mernyi said that extreme right-wing and racist crimes have risen by 175 percent between 2005 and 2013, and has complained that the government is not doing enough to address the problem.