The terrorist group announced it had destroyed six archaeological pieces confiscated from a smuggler after a hearing by an Islamic court.
It released photographs showing militants putting sledgehammers to the busts, which the terrorist group views as idolatrous.
Among the antiquities destroyed was the Lion Statue of Athena, a unique limestone piece more than 10 feet high that dated back to the 1st century BC.
The destruction "reflects the brutality and ignorance" of the extremist group and its "disregard" of Syrian culture, AFP quoted UNESCO Director-General Irina Bokova as saying on saturday.
She added that "the destruction of funerary busts of Palmyra in a public square, in front of crowds and children asked to witness the looting of their heritage, is especially perverse."
The busts not only honored the dead, she said, but they embodied "the values of human empathy, intelligence...Their destruction is a new attempt to break the bonds between people and their history, to deprive them of their cultural roots in order to better enslave them."