Human rights group Amnesty International says the victim was a 13-year-old girl who had been raped.
Initial reports had said she was a 23-year-old woman who had confessed to adultery before a Sharia court.
Numerous eye-witnesses say she was forced into a hole, buried up to her neck then pelted with stones until she died in front of more than 1,000 people... However, Amnesty said it had learned she was 13, and that her father had said she was raped by three men.
When the family tried to report the rape, the girl was accused of adultery and detained, Amnesty said.
Convicting a girl of 13 for adultery would be illegal under Islamic law.
According to Amnesty International, nurses were sent to check during the stoning whether the victim was still alive. They removed her from the ground and declared that she was, before she was replaced so the stoning could continue.
It was the first reported execution by stoning in the southern port city since Islamist insurgents captured it.
The BBC had a reporter in the area, but he was shot dead in Kismayo in June.
You know, we forget how blessed we are to live in America until we hear something as horrible as this. This girl had to endure such hideous things in her short life. I feel for her and her family.