The child, who is believed to have underlying health conditions, is among the latest confirmed deaths of people who have contracted the virus.
Where in the country the death occurred or any other details of the case have not been disclosed.
The government announced earlier that 157 additional deaths of people who tested positive for Covid-19 had been recorded in hospitals in the past 24 hours, including eight in Greater Manchester.
These were patients between the ages of 12 and 100 and of these, seven – ages 57 to 88 – had no known underlying health conditions.
The youngest death announced so far by NHS England was a six-week-old baby.
The NHS England publishes daily figures showing the dates of each coronavirus death in hospitals, including sometimes previously unreported deaths that occurred several days or even weeks ago.
This is due to the time it takes for the deaths to be confirmed as positive for Covid-19 and for the post mortem exams to be processed.
Of the 157 new deaths announced on Saturday, 30 occurred on May 22, 81 on May 21 and 19 on May 20.
Eight of them were in Greater Manchester with Salford Royal NHS Foundation Trust, Stockport NHS Foundation Trust and Wrightington, Wigan and Leigh NHS Foundation Trust each recorded two new deaths.
The NHS Foundation Trust at the University of Manchester and the NHS Foundation Trust in Bolton have each recorded a new coronavirus death.
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However, some trusts have had no new deaths.
During the daily Downing Street briefing, it was confirmed that the number of deaths in all settings, including hospitals, care homes and the community in the UK had increased by 282, bringing the total to 36,675 .
Assistant chief medical officer Dr. Jenny Harries said at the press conference that it was clear that the number of deaths “continues to decrease.”
“We will expect it to come back down,” she added.
She also said that tests for children under the age of five may take place in the future.
Currently, anyone five years of age or older can request a coronavrius test.
She said it is important that the tests are calibrated and interpreted correctly for a small child, but that “for those under five, the tests will progress in the future.”