The military Friday "uncovered a mass grave of officers, soldiers, members of the popular committees (pro-government militia) and their relatives," the source told AFP.
He said that 24 of the victims were civilians, including three children.
"They were executed either by beheading or by shooting," the source said.
The bodies have been transferred to a military hospital in the provincial capital Homs and some have been identified, he added.
On Sunday the Syrian army, backed by Russian forces, recaptured Palmyra and its UNESCO-listed ruins, which Daesh had overrun in May 2015.
During their nearly 10-month occupation of Palmyra, the extremists executed at least 280 people, according to the so-called Syrian Observatory for Human Rights, a Britain-based group which confirmed the discovery of the mass grave.