Mother on trial
Siddiqui's 12-year-old son remained in Afghan custody when his mother was flown to New York to face federal charges of assault and attempted murder.
His continued captivity prompted calls by Pakistan and rights group for his release.
"Under the presidential order of Hamid Karzai [the Afghan president], we hand over Ali Hassan, 12, to Pakistan authorities," Sultan Ahmad Baheen, an Afghan foreign ministry spokesman, said.
"We hope this step should symbolise friendly ties with our neighbouring nation Pakistan."
It was not immediately clear if Hassan would be returned to his family in Pakistan.
Separately, Pakistan's parliament has urged the US to repatriate Aafia Siddiqui who was shot in the abdomen during the incident in Ghazni province.
Until her arrest in July, Siddiqui had been declared as missing by rights groups since she left her parents' house in Karachi, Pakistan in March 2003.
Her lawyers say they believe she was held in Bagram air base in Afghanistan by US authorities.
In 2004, Siddiqui was identified by the FBI as an "al-Qaeda operative and facilitator who posed a clear and present danger to America".
Her husband was captured in 2003 and is now held at Guantanamo Bay, the US prison facility in Cuba.