The man, who worked as a cleaner in a nearby Vatican-run hospital and had a major family dispute on Wednesday, was seen by police in closed-circuit footage covered in fuel and setting light to his clothes.
Before his shocking act, the man left a note on the ground with his daughter's phone number, police sources said, adding that he may have had health problems.
He worked at Santo Spirito hospital near the main Via della Conciliazione avenue to the Vatican and is being treated at another clinic outside the city centre.
Police had initially said the man was 51.
The last time there was a self-immolation on St Peter's Square was 1998 when a 40-year-old Italian gay man set himself on fire in a protest against the Catholic Church's stance on homosexuality. He died of his wounds a few days later.