Johanna Mikl-Leitner told the APA news agency she backed the installation of a "security construction" which would allow a "controlled entry" into Austria.
"The best border crossing is worthless if its sides are wide open," she said.
"I don't really see the added humanitarian value of using (shipping) containers instead of a fence, but if it is possible to avoid the word 'fence' from a technical point of view, then that's fine by me."
The minister had sparked consternation in Brussels on Wednesday when she announced plans to build a fence stretching several kilometres on either side of the Spielfeld border crossing.
The move would deal a serious blow to the European Union's cherished passport-free Schengen zone, which counts both Austria and Slovenia as members.
Mikl-Leitner's insistence that it was time to "build fortress Europe" also appeared to be at odds with Chancellor Werner Faymann, who stressed there "won't be a fence around Austria".
Faymann -- whose Social Democrats (SPOe) form a ruling coalition with Mikl-Leitner's conservative OeVP -- told Austrian media late Wednesday that he expected the minister to present her plans in more detail.
"We need to protect (the EU's) external borders in Greece, Turkey and Italy, but definitely not in Austria," he said in a televised interview.
The EU hails the Schengen area as one of its most important achievements, and the European Commission has repeatedly expressed concern that re-imposing border controls threatens its future.
EU officials said Wednesday they were not told in advance of Austria's plan and in a sign of the sensitivity of the development, Commission President Jean-Claude Juncker held hastily arranged talks with Faymann.
The pair afterwards released a joint statement stressing that "fences have no place in Europe".
Austria and Slovenia have become key transit points for tens of thousands of refugees and migrants desperately seeking to reach northern Europe through the Balkans before winter sets in.
More than 700,000 people have landed on Europe's southern shores so far this year, the majority from Syria, Iraq and Afghanistan, and divisions have opened up between EU states about how to deal with the crisis.
Nations along the migrant trail northwards from Greece have been overwhelmed, and Hungary -- an EU and Schengen member -- has sealed its southern borders with razor wire to stop the flow.
Slovenia on Wednesday also reiterated its readiness to erect a fence along its Croatian frontier if new EU plans aimed at improving the situation fail to produce quick results.