Shaan Taseer used social media to call on people to pray for those held under Pakistan's strict blasphemy laws.
Some of those charged in the country are facing the death penalty.
His father, Salman Taseer, was murdered in 2011 after speaking in favour of law reform.
"In my Christmas message, I asked all my countryman to make a special prayer for everyone who has suffered religious persecution in Pakistan," Shaan Taseer told the BBC.
He said it was time to raise the "very basic question" of whether Pakistani citizens should be able to talk about the country's "unjust" laws on blasphemy.
"This issue has been shut down at the barrel of a gun after my father's death," he said, adding: "The law of the land states very clearly that every citizen has the right to talk about not just the blasphemy law but every law."
One of those charged under the law and mentioned in Shaan Taseer's message is Asia Bibi, a Christian woman facing the death penalty for on allegations of verbally insulting the Prophet Mohammed.
His appeal for prayers for those accused of blasphemy led to calls by an Islamic group for the state to bring charges against him under the same law. He said that he had also since received death threats.
Police in the city of Lahore said they accept the contents of the message could cause offence and are now investigating whether the video is authentic.
Members of the religious group which raised concerns over Shaan Taseer's social media post have arranged to meet government officials to discuss the case.
Shaan Taseer's father, Salman, was shot and killed by his bodyguard Mumtaz Qadri on 4 January 2011 after speaking out in favour of reform of Pakistan's strict blasphemy laws.
He was the governor of Punjab province at the time but angered Islamic hardliners by showing support for Asia Bibi, who remains on death row pending an appeal.
Qadri was later sentenced to death for the crime. Thousands of Pakistanis turned out for his funeral and he was hailed as a hero by Islamists.
Pakistan has never executed anyone for blasphemy but some of those accused have been murdered or lynched by crowds.
Most of those prosecuted under the blasphemy laws are Muslims. Some have alleged that charges against them are fabricated to settle personal scores.
The son of a Pakistani governor killed for criticising the country's blasphemy laws may face charges under the same laws after posting a video labelled "offensive" by religious groups.