Four grenades were hurled at four branches of Bangkok Bank Pcl late on Saturday, Feb 27.
Two exploded, damaging telephone booths and bank windows, and two were disposed of safely, Abhisit said.
One man got minor injury and has been sent to the nearby Leart Sin Hospital, the policeman said.
The bank has been targeted recently by anti-government protesters and supporters of the twice-elected Thaksin, who was removed in a 2006 military coup.
Thaksin now lives in self-imposed exile in Dubai after being convicted in absentia of graft.