"We will make available as many as are needed," Gerald Klug said before a cabinet meeting to discuss a range of measures to tackle the crisis including more personnel to process the migrants.
The soldiers will help in transporting people and equipment, in constructing accommodation and in providing food.
They will not immediately be deployed at Austria's borders, with Interior Minister Johanna Mikl-Leitner calling that step a "last resort".
The government also nominated a much-needed new "migration coordinator", former banker Christian Konrad.
Austria - one of the wealthier EU countries - has struggled to cope with the large number of migrants and asylum requests. Its main refugee processing centre in Traiskirchen, south of Vienna, is massively overcrowded with hundreds forced to sleep out in the open.
The federal government accuses the individual Austrian states of dragging their feet in providing extra housing.
The number of asylum requests in Austria shot up above 28,300 between January and June alone - as many as for the whole of 2014 - and officials expect the total to reach 80,000 this year.