The newborn is thought to be one of youngest victims of the disease in the UK.
The death was revealed in data announced by health chiefs on Thursday as it was reported that 135 more people had lost their lives in the UK in all settings. Of those, 62 patients had died in hospitals in England, with the eldest aged 96.
It is unclear how the baby, whose gender was not revealed, contracted the virus.
The news came as Sheffield children’s hospital confirmed that a child died on Monday after being admitted in a critical condition. The hospital, which has not confirmed the age of the child, said they had tested positive for Covid-19 but the cause of death had not been determined.
It has previously been reported that a three-day-old baby died in hospital in Bridgend, south Wales, in May after his mother contracted coronavirus. An inquest heard Coolio Carl Justin Morgan died after his mother tested positive for the disease before giving birth. The primary cause of death was given as severe hypoxic ischemic encephalopathy, meaning the brain was starved of blood and oxygen. Maternal Covid-19 was listed as a secondary cause of death.
A six-week-old baby, who had underlying health conditions, also died in May.
Previously, the youngest victim with no pre-existing health problems was believed to be Ismail Mohamed Abdulwahab, from Brixton in south London, who died in March aged 13 years.
Department of Health officials said the UK death toll was now 42,288. This figure only includes lab-confirmed patients. Figures taking into account all suspected deaths indicate the actual number of victims to be more than 50,000.
In total 20 children and young people under the age of 19 are thought to have died from the virus in hospitals in England.
It is thought that children are much less likely to suffer the most severe effects of the disease.
But doctors have been alerted to a rise in cases of an illness resembling Kawasaki disease in children. Symptoms include a sudden high temperature, rash, swollen hands and feet, dry and cracked lips and tongue, and red, sore eyes.
A study led by Imperial College London, and published earlier this month, revealed the condition to be distinct from Kawasaki, a rare but occasionally fatal disease.
Researchers said they could not be certain this new illness was caused by Covid-19, but said 45 of the 58 children involved in the study had evidence of current or past coronavirus infection. They added that the emergence of a new condition during the pandemic was unlikely to be a coincidence.