Photos of the public event were posted on Twitter by several militants’ accounts, including "Jehad News", which said the thief in the northern town of Maskanah had admitted his crimes "and also asked that his hand be cut off to cleanse his sins".
It was not immediately possible to verify the accounts. One photo showed a blindfolded man with his hand being held on a table while several militants watched, one with a large knife.
A later photo showed the man with his hand severed.
The punishment was inflicted by ISIL, mainly composed of foreign militants, an al Qaeda splinter group that is widely considered the most radical of the groups fighting President Bashar al-Assad. It is also engaged in a violent struggle with rival militant groups.
ISIL controls much of rebel-held Syria in the north. In the city of Raqqa, it has demanded that Christians pay a levy in gold and curb displays of their faith in return for protection.
It has also banned Christians from owning weapons and from selling pork or wine to Muslims or drinking wine in public.