The brazen suicide attack in Logar province, about 75 kilometres south of the capital Kabul, killed women and children and also wounded 120.
As an eyewitness described horrific scenes of victims on fire following the blast in the usually safe Azra district, officials described the attack as "unprecedented" in the near-decade-long Afghan war.
"Sixty of our countrymen including children, women, youths and men... have been martyred and 120 others including health workers have been injured," the ministry of public health said in a statement.
"This inhumane act is unprecedented in the history of the conflict in our country and targeted a place where wounds are healed and patients receive treatment." Din Mohammad Darwaish, the Logar provincial spokesman, said the blast -- which took place close to Afghanistan's border with Pakistan -- was a suicide car bombing.
The Taliban denied it was behind the attack, which completely destroyed the building. Spokesman Zabihullah Mujahid said: "We condemn this attack on a hospital... whoever has done this wants to defame the Taliban." One man who lives near the hospital, Abdul Rahman, told AFP that he lost seven relatives in the explosion.
"Seven members of my family including three women and two children went to that hospital this morning," he said, through tears.