Police said the building, in the town of Gräfenhainichen, near Leipzig in eastern Germany, had faced several attacks over the past few months.
Early on Saturday, several shots were fired at the former office block, which is being adapted to accommodate asylum applicants.
An investigation into possible attempted murder has been launched, as several security guards were in the building at the time of the shooting. No one was injured.
Several windows were damaged, and bullet holes were found in numerous places. Police said the shots were fired from a "weapon requiring a license," without giving details about the caliber of ammunition used.
Shortly after the incident, a sniffer dog was used in an unsuccessful attempt to track down the perpetrators.
The interior minister for the state of Saxony-Anhalt, Holger Stahlknecht, condemned the attack as "cowardly and devious."
Police blamed far-right groups for the attack, describing an "increasing lack of restraint among xenophobes, which the state and society will have to face to together."
Just last weekend, stones were thrown at the building, leaving glass and a billboard damaged. Several other small attacks have also seen rocks thrown.
In December, the building suffered such severe flooding that officials said it was uninhabitable. The damage was estimated at 80,000 euros ($87,450).
Last week, a spokesman for the city council said the incidents wouldn't change plans to accommodate refugees in the building.
As many as 80 people are expected to be housed there.
mm/jr (dpa, epd)