"Right now on the Austrian-German border only those seeking asylum in Germany are being allowed in. Those who want to go further are being turned back," Johanna Mikl-Leitner said on public radio Oe1.
"We will stop those people directly at our southern border (with Slovenia) from the end of next week," Mikl-Leitner said.
She also said she wants to set a limit on the number of people to be settled in Austria and introduce other steps which would make it less attractive for those seeking asylum.
Caritas President Michael Landau said he believes that turning refugees away at the border would violate people's human rights
Last year Austria became a major transit country for hundreds of thousands of migrants and refugees entering the European Union, with most travelling onwards to reach Germany or Sweden.
But last week Sweden tightened border controls, prompting Denmark to follow suit and Berlin to send back to Austria anyone not seeking asylum in Germany at a rate of 200 to 300 per day, according to Mikl-Leitner.
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Austria has already refused entry to 2,568 people entering from Slovenia since late December, according to the Slovenian authorities, because of problems with their identity papers.
German weekly Spiegel reported on its online version this week that Vienna was in talks with Croatia and Slovenia about sending Austrian police to help turn back migrants at their borders.