The prisoner swap happened on Sunday, the paper quoted the Taliban officials as saying, but it did not disclose the location.
The Taliban have established a shadow government in areas they control across Afghanistan and have even set up courts to try offenders and abide by their strict interpretation of Islamic law, or Sharia.
The development comes days after United States special envoy to Afghanistan Zalmay Khalilzad met the Taliban in Pakistan.
The Taliban have released three Indian engineers who were kidnapped in Afghanistan previous year, Taliban sources told AFP on Monday, as part of an apparent prisoner swap that saw 11 fighters released.
No individual or group including Taliban militants has so far claimed responsibility for the explosion.
One of the Indian hostages was released in March.
The release of three Indian hostages follows key meetings between US Special Representative for Afghanistan Reconciliation Zalmay Khalilzad and Taliban representatives led by Mullah Abdul Ghani Baradar in Islamabad during the weekend, the PTI report said.
The Ministry of External Affairs had then said, "We are grateful to the Government of Afghanistan for their support in securing the release and repatriation of the Indian national". Taliban leaders Sheikh Abdul Rahim, Maulvi Abdur Rashid, were also freed from Bagram airbase by U.S. forces.
In May 2018, the Taliban seized six Indian engineers who were working on a power plant project in Baghlan in northern Afghanistan, along with their Afghan driver. It wasn't clear whether the USA or Afghan forces released the Taliban.
Baradar was in Pakistan along with a 12-member Taliban delegation since Wednesday on the invitation of the Pakistan government.
The meeting is significant and the first Khalilzad has held with the Taliban since last month, when President Donald Trump declared that the talks were "dead", blaming an uptick in violence by the Taliban that included the killing of a USA soldier. Trump also cancelled a secret meeting with the Taliban and Afghan President Ashraf Ghani at Camp David near Washington.
The news came as a child rights organisation said that every single child born and raised in Afghanistan in the past 18 years has experienced and been affected by war and conflict in their country.