Islamic State, which holds parts of Syria and Iraq, seized the desert city of Palmyra in May from government forces but had initially left its ancient sites undamaged.
In June it blew up two shrines that were not part of its Roman-era structures but which it regarded as sacrilegious. It had also used Palmyra's Roman amphitheater as a place for killing people it accused of being government supporters, according to a Syria monitoring group.
The Baal Shamin temple was built nearly 2,000 years ago and its inner area was severely damaged by the explosion, which also caused surrounding columns to collapse, according to UNESCO.
"The art and architecture of Palmyra, standing at the crossroads of several civilizations, is a symbol of the complexity and wealth of the Syrian identity and history," Bokova said.
"Extremists seek to destroy this diversity and richness, and I call on the international community to stand united against this persistent cultural cleansing." (Reporting by Sylvia Westall; Editing by Mark Heinrich)