The woman, in her 40s, had warned her son that a US-backed alliance would wipe out IS and had encouraged him to leave the city with her.
She was detained after he informed the group of her comments, according to the British-based Observatory, which monitors the war through a network of local sources.
The observatory said the 20-year-old man, named as Ali Saqr al-Qasem, shot his mother, Leena, in the head with an assault rifle, near the post-office building where she worked and in front of hundreds of people.
Raqqa city is a main base of operations for the group in Syria. IS, which controls wide areas of Syria and Iraq, has executed hundreds of people it has accused of working with its enemies or of breaching of its ultra-conservative interpretation of Islam.
The observatory said she was executed under the pretext of “inciting her son to leave the Islamic state and escaping together to the outside of Raqqa, and that the coalition will kill all members of the organisation”.
The observatory reported on December 29 that IS had executed 2,000 Syrian civilians in the 18 months since it had declared its “caliphate” over the territory it controls in Syria and Iraq.
They included people killed because of homosexuality, practising magic, and apostasy.
It was not possible to independently verify the latest report.
Meanwhile, foreign special forces have been carrying out raids on an IS stronghold in northern Iraq, ahead of an offensive planned for later this year to retake Mosul, the largest city under the group’s control, Iraq’s parliamentary speaker said.
Several attacks behind IS lines, around Hawija, 210km north of Baghdad, were carried out in recent weeks, Salim al-Jabouri said.
Both the US and Iraqi military have denied that US forces have carried out military operations on the ground, in Hawija, since October, when US special forces rescued 69 Iraqis in a raid that killed one US commando.
But Dubai-based al-Hadath TV and Iraqi media have reported at least half a dozen raids in and around Hawija, since late December, led by US special forces.
Washington said last month it was deploying a new force of 100 special-operations troops to Iraq to conduct raids against IS there, and in neighbouring Syria, but didn’t provide details.