Maamoun Abdulkarim said the tombs were the 'best preserved and most beautiful' and included that of Elahbel, built in 103 AD, which he said was four storeys high and had an underground floor.
The new destruction at the world-renowned site follows the demolition of two ancient temples in the city.
The terror group, which has already blown up several ancient sites in neighbouring Iraq, took over the city in May and last month murdered its retired archaeologist Khaled Asaad, 82, who worked for more than 50 years as head of antiquities there.
ISIS went on to destroy the Temple of Baalshamin in the complex and then blew up the larger Temple of Bel days later.
Palmyra, 215 kilometres northeast of Damascus, was a jewel of the ancient world and is revered because its Greco-Roman ruins are so well preserved
Constructed in 32AD, the temple of Bel
The Temple of Baalshamin was blown up by ISIS