"For us this is the worst possible solution," said the general secretary of the Austrian Red Cross, Werner Kerschbaum, ahead of a crisis summit in Vienna.
He added that the nation, as one of Europe's richest states, had plenty of other options to accommodate migrants.
The government has already built one camp near the city of Salzburg, and is planning two more in northern Austria to help deal with the migrants who come predominantly from Syria and Afghanistan.
A record 314 asylum requests were made on Monday alone, according to official figures.
Interior Minister Johanna Mikl-Leitner defended the tent project, saying it had been the "last option" in light of the "explosive increase" in refugees in recent times.
But the Catholic charity Caritas echoed the concerns of the Red Cross and called the solution "unnecessary".
Its secretary general Klaus Schwertner believes the government may be trying to put pressure on the European Union with shock images of the migrants in the camps.
Austria, a country of 8.5 million inhabitants, is a fervent supporter of the EU's controversial migration plan launched earlier this week.
The proposal foresees the mandatory redistribution of asylum seekers across the 28-member bloc, to help ease the burden on southern nations where refugees first arrive by boat.
The scheme has been opposed by a number of countries, including Britain and Hungary.
Austria received more than 28,000 asylum requests in 2014, three times the European average relative to population size.
This year, 14,200 demands were already made between January and April.