Maamoun Abdulkarim, the head of the Antiquities and Museums Department in Damascus, tells The Associated Press that one of the tombs belongs to Mohammad Bin Ali, a descendant of Islam's Prophet Muhammad's cousin Imam Ali.
Abdulkarim said Wednesday that the tomb was just north of Palmyra.
He said the second tomb was of a Sufi scholar known as Nizar Abu Bahaa Eddine, who was in the town 500 years ago. The tomb is close to the town's famed archaeological site.
Since ISIS captured Palmyra last month, there have been fears that the extremists would blow up archaeological sites as they have in Iraq.
CBS News correspondent Clarissa Ward reported that what ISIS doesn't destroy in Palmyra is looted; trafficking antiquities is a major source of revenue for the group.
Lt. Colonel Nicholas Saad, the head of the Bureau for International Thefts in Lebanon, the country where many of those smuggled artifacts turn up, says the pieces are sold for millions of dollars.
"The people who are controlling the operation -- they will have too much money," said Saad.