Earlier today, while working at his office in Launceston, Mr Gutwein became unwell and sought medical treatment.
"He is undergoing a number of tests which to date have not identified any medical issues of concern," a statement from Jeremy Rockliff, Tasmania's deputy premier, read.
"(He) will take a few days to rest and recover."
Mr Rockliff will act as premier in Mr Gutwein's absence, while he recovers.
Appropriate arrangements are being made to cover absences from parliament this week.
Further updates on the premier's health will be released later in the week.
Mr Gutwein has served as the 46th premier of Tasmania since January 2020.
More to come.