However, Amnesty Interntional 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.
A human rights activist in the town told the BBC on condition of anonymity that he had received death threats from the Islamic militia, who accuse him of spreading false information about the incident.
He denies having anything to with Amnesty's report.
Court authorities have said the woman came to them admitting her guilt.
She was asked several times to review her confession but she stressed that she wanted Sharia law and the deserved punishment to apply, they said.
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 last week.
One of the witnesses, speaking to the BBC's Today programme, said she had been crying and had to be forced into a hole before the stoning, reported to have taken place in a football stadium.
"More than 1,000 people arrived there," he said.
"After two hours, the Islamic administration in Kismayo brought the lady to the place and when she came out she said: 'What do you want from me?'"
"They said: 'We will do what Allah has instructed us'. She said: 'I'm not going, I'm not going. Don't kill me, don't kill me.'
"A few minutes later more than 50 men tried to stone her."
The witness said people crowding round to see the execution said it was "awful".
"People were saying this was not good for Sharia law, this was not good for human rights, this was not good for anything."
But no-one tried to stop the Islamist officials, who were armed, the witness said. He said one boy was shot in the confusion.
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.
The port of Kismayo was seized in August by a coalition of forces loyal to rebel leader Hassan Turki, and al-Shabab, the country's main radical Islamist insurgent organisation.
Turki is on the US list of "financers of terrorism".
It was the first reported execution by stoning in the southern port city since Islamist insurgents captured it.
Meanwhile, Islamists in the capital, Mogadishu have carried out a public flogging.
Mogadishu is nominally under the control of government forces and their Ethiopian allies, who face frequent attacks by Islamist and nationalist insurgents.
The BBC's Mohammed Olad Hassan in the city says the flogging was a show of strength.
He says two men accused of helping to kill a man and torture his mother, who they accused of theft, were each given 39 lashes in the north-eastern suburb of Suqa-hola.
The man who actually killed the alleged thief was released, after agreeing to pay his family 100 camels in compensation.
Before the flogging, hundreds of Islamist fighters performed a military parade, our reporter says.
The BBC had a reporter in the area, but he was shot dead in Kismayo in June.