An improvised explosive device was set off just after midnight Tuesday at the Housing Finance Corporation (HFC) in Limassol, police said.
The bomb had been planted at the ground floor entrance of HFC on Vasileos Konstantinou Street, causing a fire.
Police arrived at the scene and closed off the area to carry out an investigation.
Limassol CID is working to determine the motive and identity of the perpetrators.
The extent of the damage and the cost were not immediately known.