Said to be the Taliban's overall number two, he was captured in a secret US-Pakistani raid in Karachi several days ago, The New York Times reported.
Senior officials later confirmed the report, saying Mullah Baradar was "providing intelligence".
"This operation was an enormous success," one official told ABC News.
"It is a very big deal," the official said.
The New York Times, citing US government sources, said the prisoner was the most significant Taliban figure to be detained since the US-led war in Afghanistan began in 2001.
His capture comes as Nato and Afghan troops are carrying out a major offensive against Taliban militants in southern Afghanistan.
But a Taliban spokesman denied the reports, saying Mullah Baradar was still in Afghanistan actively organising the group's military and political activities.
"He has not been captured. They want to spread this rumour just to divert the attention of people from their defeats in Marjah and confuse the public," Zabihullah Mujahid told Reuters news agency, referring to the US-led Nato offensive in the Marjah area of Helmand province.
Little is known about Mullah Baradar, but he is said to rank second only in influence to the Taliban's spiritual leader, Mullar Muhammad Omar, who has been hiding from Western agencies since the 9/11 terror attacks in 2001.
Senior intelligence officials voiced hope he would provide the location of Mullah Omar.
The BBC's North America editor Mark Mardell, in Washington, says Mullah Baradar is a "big fish" who runs the Taliban's day-to-day operations, both military and financial.
He allocates Taliban funds, appoints military commanders and designs military tactics, our correspondent says.
Mullah Baradar was quoted last year as telling his troops not to confront US soldiers with their superior firepower, but to operate using guerrilla tactics.
He is said to be responsible for the Taliban tactic of planting "flowers" - improvised explosive devices (IEDs) - along roadsides.
The New York Times said the Karachi raid was conducted by Pakistan's Directorate for Inter-Services Intelligence (ISI) and CIA operatives, citing officials.
The newspaper said it learned of the operation on Thursday, but delayed reporting it after a request by White House officials. They said disclosing it would end a very successful intelligence drive.
US officials later acknowledged the news, saying it was becoming broadly known in the region.
According to Interpol Mullah Baradar was born in 1968, and served as deputy minister of defence for the Taliban regime in Afghanistan before it was toppled in 2001.
He has been subject to UN sanctions including a travel ban, an arms embargo and the freezing of assets.
Although little is known for certain about Mullah Baradar, he was reported to have engaged in an e-mail exchange with Newsweek magazine in July 2009, in which he vowed to "inflict maximum losses" on US forces in Afghanistan.
"In every nook and corner of the country, a spirit for jihad is raging," the magazine quoted him as saying.
