Education Minister Heinz Fassmann said that the draft law would be ready by the summer. He added that it would be a "symbolic" act, regardless of how many children were actually affected.
Vice-Chancellor Heinz-Christian Strache of the far-right Freedom Party (FPÖ) had floated the idea of a ban over the weekend, saying that girls "under the age of 10 must be protected" and be able to "integrate and develop freely".
Chancellor Sebastian Kurz of the centre-right People's Party (ÖVP) also backed the idea, telling the Oe1 radio station: "We want all girls in Austria to have the same opportunities", and that he wanted to avoid the development of "parallel societies".
The Kurier newspaper reported that neither the education ministry nor various experts asked by the paper were able to provide figures for how many girls currently wear the headscarf in kindergartens and primary schools.
Carla Amina Baghajati, spokeswoman for the Islamic Religious Community in Austria, called the debate over the headscarf "a marginal issue", which had been given disproportionate attention.
Any schools affected by the issue should be engaged in "dialogue", she said.
Debates around immigration and identity were central to last year's election campaign which resulted in Kurz becoming chancellor after agreeing a coalition pact with the FPÖ.
Austria received more than 150,000 asylum applications -- almost 2 percent of its total population of 8.7 million -- following the migration crisis of 2015.