Sarah Courtney has contracted COVID-19 and is isolating in France after a positive PCR test result, Mr Gutwein revealed on Wednesday.
Public school students return to the classroom on February 9, with the state government rolling out COVID-19 packs to all children and fixing some 8000 classroom windows for better ventilation.
Mr Gutwein said he hoped Ms Courtney, who he said was due to fly back to Tasmania on Wednesday or Thursday, would be back at work before term one.
Mr Gutwein said he approved her leave and defended the timing, saying it was "perfectly appropriate" for ministers to have a break.
"To be frank I'd be happy to have a debate with anybody in respect to whether or not a minister should have an appropriate break," he said.
"I know myself, late last year, what can happen if you don't take a break."
Mr Gutwein was in December hospitalised with a mystery illness later put down to overwork.
He said Ms Courtney was fatigued and had a slightly croaky voice but was feeling well and would finish her seven-day isolation on Sunday.
The education portfolio has been picked up by Jeremy Rockliff who is also the health minister.
The state Greens have called on Ms Courtney to resign when she returns from France, calling her decision to take leave foolish and inexcusable.
"Like Scott Morrison heading to Hawaii while the country was on fire in 2019, Sarah Courtney abrogated her responsibility just when leadership in the portfolio is most needed," leader Cassy O'Connor said in a statement.
Labor opposition education spokesman Josh Willie told media it was vitally important Ms Courtney was on hand to deal with any issues.
Mr Gutwein says he expects case numbers to rise when students return.
He said schools would receive back-to-school packs, containing two rapid antigen tests and masks, by the end of the week for distribution.
Tasmania recorded 666 new COVID-19 cases on Wednesday, with the number of people in intensive care increasing from one to two.
There are eight people being treated in hospital specifically for the virus, the same as Tuesday's figure. Another five cases are in hospital for unrelated medical conditions.
Tasmania recorded 504 new infections on Monday and 699 on Tuesday.
There are 3876 documented active cases statewide, continuing a broad downward trend over the past few weeks.
Mr Gutwein said the state's four major public hospitals had been downgraded from COVID-19 escalation level three to two due to easing virus pressures.
"It enables a safe and staged return to business as usual, including surgical services and ... a relaxation of some visitor restrictions," he said.
Tasmania has reported 18 coronavirus deaths since the beginning of the pandemic, with five of those occurring since borders reopened in mid-December.
16°C