"Austria cannot tolerate that," Foreign Minister Sebastian Kurz told his Hungarian counterpart Peter Szijjarto, a day after Budapest announced it was opting out of the Dublin Regulation.
Hungary has said that it is overburdened by illegal immigration - more than 60,000 people have entered the country illegally this year, according to government officials.
Many try to continue on to other European states but under the EU's Dublin Regulation those countries can return asylum seekers to Hungary to have their application processed there.
Just days ago Hungary announced it would erect a border fence against migrants.
Kurz said it was "unacceptable" that a neighbouring country should suspend the core principle for handling asylum claims in the EU.
Speaking to Szijjarto on Tuesday evening, he said that he warned him that Hungary's decision will have "negative consequences".
The EU has called on the Hungarian government to immediately clarify its position.
"We all wish for a European solution, but we need to protect Hungarian interests and our population," a spokesman for the Hungarian government told Austrian media.
Austria is the country most affected by Budapest's move, with most of the migrants on its territory arriving either from Hungary or Italy.