According to its author, Ednan Aslan, a Turkish-born Austrian professor at Vienna University, some 10,000 children aged two to six attend around 150 Muslim preschools, teaching the Koran much like Christian ones do with Bible studies.
At least a quarter are backed by groups propagating arch conservative strains of Islam like Salafism, or organizations that see religion not just as a private matter but integral to politics and society, Aslan believes.
"Parents are sending their kids to establishments that ensure they are in a Muslim setting and learn a few suras (chapters from the Koran)," Aslan, a respected researcher into Islamic education, told AFP.
"But they are unaware that they are shutting them off from a multicultural society," he said.
The study, published last year, has been jumped on by critics of immigration - not least the far-right Freedom Party - in the wake of attacks such as Paris and Brussels perpetrated by Muslims who grew up in Europe.
But many reject Aslan's findings, questioning its methodology.
The magazine Biber, which writes for and about minorities, sent a veiled Muslim reporter undercover posing as a mother looking for a place for her son at 14 Muslim kindergartens.
She found no evidence to back up Aslan's suggestions that they were churning out "little Salafists" or that things like the children singing - frowned upon by ultra-strict Muslims - were banned.
But around a third were according to the magazine "problematic", "cutting off or isolating children" from mainstream society. It also voiced concerns about the "openness" of some staff and the level of German spoken.
Vienna City Hall has since sought to calm the situation by commissioning an in-depth study involving a six-strong research team which will be published later this year.
But the first problem is establishing how many Islamic kindergartens there are. Vienna has 842 registered kindergartens, 100 of them Catholic-run and 13 Protestant, but the number of Muslim ones is not known.
Part of the reason is that there has been an explosion in the number that are privately run, stretching the ability of the authorities to keep tabs and allowing some to operate under the radar.
City of immigrants
Vienna is home to 1.8 million people, half of whom have a parent born abroad or who were born abroad themselves. Ever since it was the capital of a vast empire, it has been a magnet for outsiders, not all of them always welcome.
"But what is new in recent years has been the religious aspect of the debate about integration," said Thomas Schmidinger, political scientist and Islam specialist at Vienna University.
Austria, a nation of 8.7 million people, has received more than 130,000 asylum applications since 2015 following the onset of the European Union's biggest migration crisis since World War II.
The Freedom Party is riding high in the polls. Surveys suggest that public attitudes to Muslims have hardened. Attacks on migrant shelters soared last year.
The ruling centrist coalition has moved to the right with plans to ban full-face veils in public and oblige migrants to sign an "integration contract".
Organizations representing Austria's 700,000-strong Muslim population say that in this context, Aslan's flawed report has only fanned the flames.
"This study feeds populism and forces Muslims to justify themselves constantly," said Murat Gurol from newly created pressure group the Muslim Civil Society Network.
The 45-year-old IT worker said he sent his own son to a Muslim kindergarten in order to learn "the values of solidarity, humanity and responsibility".
As a child he went to a Christian preschool, and "I don't see why that should be allowed for one religion and not for another", he told AFP.
By Sophie Makris