Ms Courtney, who held the health portfolio when the COVID-19 pandemic struck, says she wants to spend more time with family after a gruelling few years.
"I am resigning as both minister and member for Bass," the Liberal MP told reporters on Thursday.
"I have given my heart and soul to this role for eight years and have taken every step to ensure it is my first priority.
"However, I believe the time has come for me to move on.
"When I was on leave, it gave me the opportunity to properly consider what future is personally right for me and my family."
Ms Courtney contracted COVID-19 while overseas and returned to Tasmania this week.
She was criticised by the Labor opposition and Greens over the timing of her leave but had the backing of Premier Peter Gutwein.
Ms Courtney said her decision to resign, which came on the second day of term one, was not based on the criticism.
She said she would travel to Sydney on Friday for the funeral of her grandmother, who died while Ms Courtney was in isolation overseas.
"The past two years in particular have been especially gruelling. Rewarding, but very gruelling and exhausting," she said.
"I don't accept the criticism that has been put forward by Labor and the Greens. I think it is unfounded."
Ms Courtney was elected to parliament in 2014 and holds five portfolios, including tourism, hospital and events and disability services.
In October 2018, she stepped down as primary industries minister after informing then-Premier Will Hodgman she was in a relationship with the secretary of a department she was overseeing.
An inquiry cleared Ms Courtney and Department of Primary Industries, Parks, Water and the Environment head John Whittington of any wrongdoing.
The pair have since married.
Her decision to quit comes less than a year after she was re-elected as one of three Liberal members in the five-seat northern electorate of Bass.
In a cabinet reshuffle following the May 2021 state poll, Ms Courtney relinquished the health portfolio and was appointed education minister.
A recount will be held in Bass, with Ms Courtney's seat all but certain to go to one of three Liberal candidates - Simon Wood, Greg Kieser or St Vincent de Paul state boss Lara Alexander.
Candidates have until noon on February 25 to nominate for the recount, which will begin shortly afterwards.
The Liberals hold 13 seats in the 25-member lower house.
Mr Gutwein said he would mull a cabinet reshuffle over the next week.
He said Ms Courtney had been a fantastic member of parliament who carried an "enormous weight" during the state's most difficult moments of the pandemic.
Australian Education Union Tasmania president David Genford says she leaves behind a poor legacy.
He said a serious shortage of teachers and support staff must be urgently addressed.
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