Ali Saqr, 20, had reported his mother, Lina, to IS authorities in Raqa "because she tried to persuade him to leave IS and flee the city," the Syrian Observatory for Human Rights said.
Authorities subsequently arrested the woman and accused her of apostasy, the monitoring group said.
On Wednesday, she was shot to death by her son "in front of hundreds of people close to the mail service building in Raqa city," the Observatory added.
The incident was widely condemned online by social media users.
Raqa is the de facto Syrian capital of IS's so-called "caliphate," the territories it controls in Syria and Iraq where it imposes its harsh interpretations of Islamic law.
Among the crimes that warrant a death sentence in IS territories are homosexuality, "exposing jihadist genitalia," adultery and intercourse with animals, according to the Observatory.
Other acts punishable by death range from blocking roads to "betraying Muslims" and working with anti-IS groups including the "crusader" US-led coalition.
But in IS-held territories, using child soldiers and "owning slaves", which are typically sexually abused, are both legal.
And the extremist group has been accused of carrying out mass killings, torture, rape and sexual slavery.
A US-led coalition has been striking the jihadists in Syria and Iraq for over a year.
More than 260,000 people have been killed in Syria's war since it erupted in March 2011.
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