No further influenza A cases have been reported in Launceston General Hospital since Saturday night.
However, Tasmanian Health Service Executive Director of Operations Eric Daniels said the result could change as testing was ongoing to determine whether other patients have been infected.
Six cases of influenza A were confirmed in ward 6D, with testing protocols still in place.
Mr Daniels said the results were likely to be known on Tuesday.
“Additional cleaning is being conducted to prevent further spread of the virus.”
The hospital was forced to stop admissions to the general medical ward because of the number of cases of influenza A on Friday.
By 3pm that day, three cases had been confirmed with four others suspected.
Mr Daniel reminded visitors that entry to the ward was being restricted while infection control remains a priority.
He advised anyone suffering from influenza or influenza-like symptoms, which include fever, dry cough and fatigue, to avoid visiting patients.