Al-Jazeera said that Taleban leader Mulla Mohammad Omar had been invited as the guest of honour, but had not attended. He sent several of his aides to represent him instead.
It said the wedding took place in the southern city of Kandahar on Tuesday.
The younger bin Laden was shown wearing traditional white Arab headdress sitting on a carpet between his father and another man believed to be the bride's father Abu Hafas al-Masri.
Two armed bodyguards could be seen in the background.
Mr Masri is an Egyptian aide to Mr Bin Laden who fought with him against Soviet forces in Afghanistan.
The film, which Al-Jazeera said was shot exclusively in Afghanistan, did not show any pictures of the bride.
Al-Jazeera said that Taleban leader Mulla Mohammad Omar had been invited as the guest of honour, but had not attended. He sent several of his aides to represent him instead.
Mr Bin Laden, a wealthy Saudi dissident, who was given refuge in Afghanistan by the ruling Taleban movement, has been indicted by the United States for the bombing in 1998 of the US embassies in Nairobi and Dar es Salaam which killed more than 200 people.
Days after the bombings, the USA fired dozens of cruise missiles on eastern Afghanistan in an attempt to kill him.
A senior Yemeni security official said on Tuesday that a suspect facing trial in connection with the attack on the US destroyer Cole last October had said he believed Mr Bin Laden gave the orders for the Cole attack.
Seventeen US sailors were killed in what is believed to have been a suicide bombing.
Mr Bin Laden has denied involvement in the attack.
The United Nations decided last month to impose fresh sanctions on Afghanistan to press the Taleban to hand him over for trial.