The lyrics in the book produced in 1997 by the Germania zu Wiener Neustadt organisation included "Step on the gas... we can make it to seven million", media reports said.
Six million Jews were killed in the Holocaust during World War II, many of them in gas chambers.
Other songs in the book, which only became public last week, praised the Waffen SS and Nazi paratroopers behind war crimes committed in Greece.
The scandal took on a political dimension because until recently the fraternity's vice-chairman was Udo Landbauer, a candidate for the far-right Freedom Party (FPOe) in local elections in Lower Austria state last Sunday.
It also put Chancellor Sebastian Kurz under pressure since he had formed a coalition at federal level in December with the anti-immigration, Islamaphobic FPOe.
Several leading members of the FPOe -- a party created by former Nazis in the 1950s -- belong to student fraternities, many of which believe in reunifying Austria into a "Greater Germany".
The FPOe says the fraternities are harmless, with its leader Heinz-Christian Strache saying on Friday that "anti-Semitism, totalitarianism (and) racism are the opposite of fraternity thinking".
Only joking
The affair has also embarrassed the centre-left Social Democrats (SPOe) after it emerged that a party member -- one of four people under investigation by prosecutors -- had illustrated the song book.
The unnamed man, since expelled by the party, said Wednesday that his drawings had nothing to do with the verse about gas chambers and that the song in question was meant as a "joke".
"The pictures show scenes of students, drinking beer or celebrating. There are also soldiers because there are corresponding songs in the book," the 70-year-old fraternity member told local media.
"But what this is not is a Nazi songbook... This stupid verse was discovered at some point and blacked out, about 20 years ago. Basically the song is a joke song... It was never sung."
The FPOe, however, has not ejected Landbauer. The 31-year-old has said he was 11 years old when the book was printed and only found out about it last week.
"You can imagine what decision I would make if this was in the OeVP," Kurz said on Wednesday as he announced the government's aim to disband the fraternity.
The Austria Press Agency meanwhile quoted a lawyer as saying that the government might find it hard to dissolve the fraternity unless it could be proven that the song was actually sung.
Interior Minister Herbert Kickl, who is from the FPOe, said in a statement that the fraternity would be disbanded "if criminally relevant activities are established... Mere suspicions are not sufficient."
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