Ali Haider Gilani was kidnapped last year during the election campaign in May from Multan.
In the video, Ali is said to have said that he was not in the custody of the Taliban.
The information on the video was revealed by Interior Minister Chaudhry Nisar Ali Khan in an "informal" interaction with some journalists.
An Interior Ministry spokesperson later said the video was not sent to the government and asked the media to be sensitive while reporting on the matter.
Ali said in the video that if measures are not taken for his release within one month he will be killed.
In August 2011, Shahbaz Taseer, the son of late Governor of Punjab Salman Taseer, was kidnapped from Lahore. Both the kidnappings have been linked to the outlawed TTP.