The baby was born at the Max Super Speciality Hospital in Shalimar Bagh, New Delhi, last Thursday but pronounced dead two hours later, the boy's grandfather, Praveen Malik, told CNN.
His mother had given birth to twins but the girl was declared stillborn.
The parents were on their way to a cremation ground when they noticed "some movements" inside one of the polythene bags that the hospital gave them with the babies' bodies.
"When we opened the bag, we found the boy breathing. I was shocked. I couldn't believe my eyes," Malik said.
The hospital previously said in a statement that the boy was "handed over without any sign of life" by the hospital staff.
The boy is still in a critical condition in hospital, according Dr. Sandeep Gupta, from the Delhi New Born Centre where the baby is now receiving treatment.
"He is on ventilator support, nutrition support and other supports. We are managing to maintain his vitals at the moment but the condition is very serious," Gupta said.
Max Healthcare said in a statement released late Sunday evening that the decision to let the two doctors go should not be interpreted as an admission of guilt.
"We wish to clarify that this action should not presuppose finding of any lapse by the expert group and should not be construed in any way to be anything other than an expression of our continued commitment to providing quality healthcare," the statement from Max Healthcare said.
An investigation by an external group of experts is expected to be concluded Monday.
Delhi Chief Minister Arvind Kejriwal also tweeted saying authorities would take the "strongest action" if someone is found at fault.
"We want the Delhi government to take strict action against the hospital authorities for their negligence," the boy's grandfather said.