Her death was first reported by The Sun.
Jones, 48, who had no previous military training, had been used to recruit Western girls to the group and posted threatening messages to Christians in the UK.
She used her Twitter account to provide practical advice on how to travel to Syria.
Previously a punk musician, Jones married the jihadist computer hacker Junaid Husain, who was killed in a drone strike in 2015.
Major General Chip Chapman, the former Ministry of Defence head of counter terror, said Jones would have been a “significant” target as a result of her alliance with Hussain and her role in recruiting IS fighters.
Responding to reports her son was killed in the strike, he added: “It is a difficult one because under the UN Charters he is under the age of what we would classify as a soldier.”
A Foreign Office spokeswoman said: “We do not comment on matters of national security.”