Two deaths at Burnie's North West Regional Hospital have been referred to the coroner.
Health authorities say a man died on Sunday morning and a woman early on Monday.
Both were aged in their 60s.
The pair had previously tested positive to Covid-19 but also had serious unrelated health conditions.
"Until more information relating to the deaths is obtained from the Coroner, they will not be counted as coronavirus-related deaths," said Deputy Director of Public Health, Dr Scott McKeown.
"Tasmania’s coronavirus-related deaths remain at 13, depending upon the outcomes of the Coroner’s determination."
The state went a third day without a new infection on Monday, leaving the infection total on 226.
Health Department figures state just 16 active infections remain in the state, including seven hospital patients.
AAP Image/Simon Sturzaker