Baradar, considered the most influential Taliban leader, second only to Mullah Muhammad Omar, was arrested in Karachi in mid-February in a secret joint operation by Pakistani and U.S. intelligence forces. It was several days after his capture before news of the arrest was made public.
The Lahore High Court also banned extraditing four other unnamed Taliban chiefs reportedly seized recently, the BBC reported.
The order was in response to a petition filed by a rights activist to prevent the detainees from being sent abroad.
"The high court has ordered that none of the leaders should be handed over to the (United States) or Afghanistan," Tariq Asad, a lawyer handling the petition, told the BBC.
"The court has also said that none, other than Pakistan intelligence or security officials, should be given access to the Taliban leaders," he said.
Details of Baradar's capture "remain murky," The New York Times wrote at the time. But officials said that it had been carried out by Pakistan's military spy agency the Directorate for Inter-Services Intelligence with CIA operatives helping out.
The news that Baradar will not be extradited comes as India's prime minister said he had asked Saudi Arabia's King Abdallah to use his influence to persuade Pakistan to stop abetting terrorists on Indian soil.
"I know Saudi Arabia has close relations with Pakistan," Prime Minister Manmohan Singh told reporters on board the special aircraft in which he and his delegation were returning to India after a three-day visit to Saudi Arabia.
"I did discuss Indo-Pakistan relations on a one-to-one basis with (the king)," Singh is quotes as saying by The Times of India.
"I explained to him the role terrorism, aided, abetted and inspired by Pakistan is playing in our country. I did not ask him to do anything other than use his good offices to persuade Pakistan to desist from this path."
The Times report noted that Singh, while addressing the Majlis Al-Shura, the Saudi legislature, said that if Pakistan cooperated with India, no problem would be insurmountable "and we can walk an extra mile to open a new chapter in relations between our two countries."
But Pakistani President Asif Ali Zardari was on the offensive even as Singh as retuning from Saudi Arabia.
Zardari said that his country is focusing on strong international alliances, a functioning society and a vibrant economy. He also said, writing in a column in London's Guardian newspaper, that no one should underestimate the resolve of Pakistan to fight terrorists.
"Terrorists do not want Pakistan to succeed," he said. "They want to distract us from preparing for a stable and prosperous future."
Zardari's reassurances can be seen in light of questions being asked by its allies of Pakistan's commitment to arrest terrorist suspects. Some U.S. officials said that Pakistani officials could have arrested Baradar at any time.
However, the participation of Pakistan's spy service suggests a new level of cooperation from Pakistan's leaders, the Times wrote. Even Pakistan's chief of army, Gen. Ashfaq Parvez Kayani, now says they can no longer support the Taliban in Afghanistan, as they have quietly done for years, without endangering themselves.