Jersey's government reported that the patient was in their 70s and had significant underlying long-term health conditions and had been under the care of the health authorities for some time.
The island's chief minister, Senator John Le Fondre, said he was very saddened to hear of the death, and underlying health conditions do not make loss of life any easier.
Jersey health minister Deputy Richard Renouf said his thoughts were with family and friends.
'It is devastating to lose a loved one and all of us in health and community services are saddened by this loss.
'We would like to offer our condolences and will not be releasing any further details about this patient, to protect their confidentiality.
'We will continue to update islanders on the numbers of people who have been tested for Covid-19, the number of people who have contracted the virus and any other relevant information as soon as this information is confirmed.'
Late today [Sunday] there has been 45 positive diagnosis of Covid-19 in the Bailiwick of Guernsey, an increase of six on Saturday's total, and 61 in Jersey.
At the Princess Elizabeth Hospital there are three patients with coronavirus, but the positive news is that they have not needed to enter the ICU.
In total there have now been 537 test samples taken in the Bailiwick, 70 people are waiting for the results and 32 people are waiting to be tested, down from 90.
The majority of the positive cases are due to overseas travel, meaning that people have arrived into Guernsey with the disease.
It has been estimated that there are 1,439 islanders under compulsory self-isolation, which equates to 2.2% of the population.