The Sindh home department received instructions from the federal government, which includes the postponement of Mirza's execution, the channel reported.
Sources said that Mirza's death sentence was an issue for the MQM, who have expressed fears that political activists on death row could be executed by military courts.
The sources further stated that the decision to postpone the execution was taken by the government to allay the MQM's fears on this issue.
Mirza was sentenced to death by an anti-terrorism court in May 1999 for murdering the managing director of then named Karachi Electric Supply Corporation Shahid Hamid, his driver Ashraf Brohi and guard Khan Akbar in July 1997.
He was moved along with four high-profile prisoners to the Machh jail, Balochistan, in April 2014.
In May last year, Mirza's brother petitioned the high court to move him to a Karachi prison.
He argued that his brother had been shifted to the Machh jail without the orders of the competent authority or any notification.
The petition had been disposed of by provincial authorities on the pretext of security reasons.