Despite the fall of the self-proclaimed ISIS "caliphate" in 2019, the group continues to launch deadly attacks from hideouts in the Syrian desert, which extends from the outskirts of the capital Damascus to the Iraqi border.
The Observatory, which relies on a network of sources across the country, said the death toll could rise as most of the wounded soldiers were in a serious condition.
ISIS did not immediately claim responsibility for the attack.
Syrian soldiers are occasionally moved across country by bus, a high-risk mode of transport given the large concentration of men within a single unarmoured vehicle.
In October, 27 Syrian soldiers were killed when a bus in Damascus was blown up by two bombs. Two similar attacks in central Syria and in Damascus in January killed eight soldiers.
Palmyra, which has a Unesco World Heritage site that includes Roman ruins, was seized by ISIS in 2015 at the height of the country's civil war.
The city was retaken in March 2016 after Russia's intervention to assist President Bashar Al Assad, only to fall back into ISIS hands in December 2016, before again being recaptured by government forces in January 2017.