The suggestion by Deputy Mayor Anja Hagenauer follows weeks of debate over the burqini ban on French beaches, that was suspended last week by the country's highest administrative court.
Hagenauer has said a ban on headscarves is not legally possible but says she is making an “urgent recommendation” for parents not to send their daughters to kindergarten wearing headscarves.
“It is not about banning something religious,” she told the ORF, adding that wearing the headscarf suggests the child “is being looked at by men in a lustful way” and could be seen as a “sexual object”.
There are around 2,300 children are cared for in the city's kindergarten facilities, with around a fifth from Muslim families. It is not known how many children in this age bracket actually wear headscarves to kindergarten.
Hagenauer added that she does not want some four or five-year-old girls being treated differently to others, such as not going into a paddling pool or being able to do sports activities.
She added that she would also consider a similar initiative for secondary schools in Salzburg.
Politicians debate veils and burqas in Austria
It follows the decision by France's highest administrative court to suspend the burqini ban introduced in dozens of French seaside towns, which supporters said was "necessary, appropriate and proportionate" to prevent public disorder after a succession of jihadists attacks in France.
Hagenauer's comments are the latest from Austrian politician concerning women wearing veils.
In August several Austrian politicians signalled their support for a full or partial ban on full face veils in recent weeks, including Foreign Minister Sebastian Kurz who said recently he believed the burqa is “a hindrance for integration”.
Interior Minister Wolfgang Sobotka also said he can imagine banning burqas for “car driving, on entry, or at demonstrations”, although he is against a full ban on face veils.
However Green politician Ahmet Demir provoked an angry reaction online after posting a photo of two nuns wearing habits and sarcastically joking they were ‘oppressed women' wearing burqas.
Demir later said he was making that point that “every woman should be able to wear what they want as long as they chose the clothes themselves”.