Previously, the youngest person to have died with the virus in the UK with no pre-existing health problems was Ismail Mohamed Abdulwahab who was 13 and from Brixton in south London.
In May, a 6-week-old child who did have underlying health conditions died.
In a statement, the hospital said: "Sadly, on Monday, June 15, a child passed away at Sheffield Children's having been brought in to the hospital in a critical condition.
"Attempts at resuscitation were unsuccessful.
"The cause of death is not yet known. Tests have confirmed that the child had Covid-19, but it isn't yet clear if it was a contributing factor."
• Covid19.govt.nz: The Government's official Covid-19 advisory website
-Additional reporting, NZ Herald