The party controls five government ministries.
Gottfried Waldhäusl said the law was designed "from an animal welfare point of view."
Far-right Austrian Vice Chancellor Heinz-Christian Strache is on the losing end of a court ruling after he accused left-wing activists of of "public insults."
The Freedom Party pursues a policy of "Austria first," and is opposed to Islam and immigration.
The law would allow authorities to stop providing food and shelter in measures seen as countering the rise of the far-right Freedom Party.
Freedom Party chief Heinz Christian Strache says legislation is needed to outlaw Muslim symbols, similar to an anti-Nazi law on the books.
The far-right Dutch politician said Europe was "imploding" due to weak leaders and open borders.
The far-right Freedom Party narrowly lost but the election will now have to be rerun.
Country may be set to elect the EU's first hard-right head of state.
If an election were held tomorrow, the party would be the largest in the Dutch parliament.