The newborn caught the virus through the placenta while he was in his mother’s womb.
But the mum had not been displaying Covid-19 symptoms and had no idea she was carrying the disease.
Doctors are said to have discovered both mum and baby had coronavirus during hospital tests, when results came back positive.
The baby boy is said to be doing “well” after he was born by C-section yesterday at the Alto Mayo hospital in Moyobamba, in the country’s northern San Martin Region.
The pair have been quarantined in the hospital and friends and relatives of the mum who have been in close contact with her over the past couple of weeks are to be tested.
Alvaro Bardalez, director of a regional health organisation, has described the newborn as the first child to be born with coronavirus in Peru and the only the second in the world.
It comes after a newborn baby tested positive for coronavirus in England last month.
Mr Bardalez said: “The mother and her baby boy are stable and doing well.
“The newborn has a good weight for his age and is drinking his mother’s milk. He’s okay.”
He added: “The mum came to hospital for a programmed caesarian and we only discovered she had coronavirus when she was tested just before giving birth.
“She had no symptoms that indicated she had Covid-19.
“Part of the protocol we’re following is that she’s wearing a face mask at all times.”
Medics say they have ruled out a transfer to the Peruvian capital Lima for the time being.
Last month it emerged a newborn baby in England, described then as the world’s youngest victim, had tested positive for coronavirus.
The child’s mother had been rushed to a London hospital days earlier with suspected pneumonia.
The mum was tested at North Middlesex Hospital but her positive result was known only after the birth.
The baby was tested within minutes of arrival.
North Middlesex university hospital NHS trust said after the case emerged: “Two patients at North Middlesex university hospital have tested positive for coronavirus.
“One has been transferred to a specialist centre and one is being treated in an isolation room.”
Yesterday a heavily-pregnant nurse who died with coronavirus after her daughter was born by C-section, was named as Mary Agyeiwaa Agyapong, 28.
Mary died at Luton and Dunstable Hospital on Easter Sunday. It is not yet clear if her newborn daughter, also called Mary, has coronavirus.
Peru’s Health Ministry said the number of confirmed coronavirus cases in the country stood at 11,475 and the number of Covid-19 deaths at 254.
Nearly 150 of the 1,113 currently hospitalised are in intensive care.