"Schengen is on the brink of collapse," Mikl-Leitner was quoted as saying by the Guardian.
Earlier, on Monday, EU interior ministers held talks on the possible extension of temporary border controls in the Schengen area to tackle immigration.
Several Schengen member states have reintroduced border controls to curb migration inflow, including Austria and Germany, which is among the main destinations for people fleeing conflict-torn areas in the Middle East and North Africa.
The reintroduced border checks are due to expire in May, at which point the countries will be obliged to either lift the measures or extended them for a maximum period of two years.
Under current Schengen rules, a EU member country is allowed to restrict entry only temporarily. Free travel within the bloc is a fundamental principle of the European Union.
