Police are now offering a €5,000 reward for information that leads to the seizure of those responsible.
The huge fire broke out in the early hours of Wednesday in the village of Altenfelden and left only charred remains of the building.
No one was harmed in the blaze, which was battled by up to 200 firemen.
"We found two sources along the building's outer walls... where unknown suspects are thought to have started the fire," police said in a statement, adding that investigations were ongoing.
The alleged attack happened two weeks before 48 asylum-seekers were due to move in.
Austrian Interior Minister Wolfgang Sobotka condemned "all forms of violence against refugee centres" while Foreign Minister Sebastian Kurz said in a tweet that he was "deeply affected" by the blaze.
Sobotka added that an investigation was underway.
The Red Cross, which operates the centre, said it was "shocked".
"We will nevertheless carry out our duty to aid people looking for help and will seek out discussion with the regional authorities in the coming days to rebuild the centre as soon as possible," Red Cross president Walter Aichinger said.
The organisation estimates the damages to be around €300,000.
"We have no indications at all that people in the village were at all unhappy," Red Cross spokesman Stefan Neubauer told AFP.
Austria has so far been spared the string of arson attacks on refugee centres seen in neighbouring Germany, but many people are unhappy about the arrival last year of 90,000 asylum-seekers in Europe's biggest migrant influx in decades.
Last week, police commandos arrested a suspected neo-Nazi who told friends he wanted to "kill all asylum-seekers", recovering several weapons and ammunition at his home.
In May, a candidate from the far-right Freedom Party (FPÖ) came within a whisker of being elected to the largely ceremonial but coveted presidency, losing by just 31,026 votes to an ecologist independent.
This story has been updated to reflect confirmation of arson by police.