He was found in the River Taff close to Taffs Mead Embankment last week.
At a press conference on Tuesday, a midwife from Cardiff and Vale health board issued a plea to the baby's mother, who has not yet been found.
Suzanne Hardacre said: "Our midwives and doctors are worried about you and understand you have been through a very traumatic time."
She said the team understood the mother may be frightened to come forward, but said any care she received would be in confidence.
"We are aware that this must have been a very difficult and distressing time for you and we are not here to judge you," she added.
Det Insp Mark O'Shea of South Wales Police said: "An interim post mortem has been conducted and the baby died at childbirth."
The baby boy who was found in a Cardiff river is believed to have died at birth, police have said.