The fatality in the week June 12 to 18 took the total number of coronavirus-related deaths recorded by the Northern Ireland Statistics and Research Agency (Nisra) to 2,980.
It is the second time in three weeks when just one death has occurred in a seven-day period.
Prior to that, the last time Northern Ireland registered such a low weekly death toll was in July last year.
The department’s statistics focus primarily on hospital deaths and only include people who have tested positive for the virus.
Nisra obtains its data from death certificates on which Covid-19 is recorded as a factor by a medical professional, regardless of where the death took place or whether the patient tested positive.
The statistics agency reports its Covid-19 data with a week lag.
The department’s death toll stood at 2,155 on June 18.
Of the 2,980 deaths recorded by Nisra by June 18, 1,973 (66%) occurred in hospitals, 776 (26%) in care homes, 14 (0.5%) in hospices and 217 (7%) at residential addresses or other locations.
Nisra reported that up to June 18, the deaths of 1,013 care home residents were linked to Covid-19.
The figure includes the 776 deaths that took place in care homes, and a further 237 care home residents who died in hospital having been taken there for treatment.
Care home residents make up about 34% of deaths linked to Covid-19 in Northern Ireland, according to Nisra.
In the week of June 12-18, one coronavirus-linked death was officially registered in Northern Ireland. That fatality could have occurred before that week as deaths can take a number of days to register.