The move came on the same day the state government revealed several senior hospital figures grilled at an inquiry into child sexual abuse would retire.
The state government originally planned to deliver the apology in parliament on October 18, following the conclusion of public hearings in a child sexual abuse inquiry in mid-September.
The inquiry is examining abuse allegations in state institutions, including health, education, justice and out-of-home care.
Survivors and whistleblowers who gave evidence at the inquiry pointed out on social media that October 18 was the three-year anniversary of the death of pedophile nurse James Geoffrey Griffin.
Griffin, who worked in the children's ward at the Launceston General Hospital for almost two decades, took his own life in 2019 after being charged with multiple child sexual abuse offences.
The inquiry was told of missed red flags surrounding Griffin, including reports made to police, and of "catastrophic" failures in the hospital's handling of investigations after his death.
A state government spokeswoman on Friday said the apology had been moved to October 25.
Media coverage of allegations against Griffin was a major catalyst for the calling of the inquiry in late 2020.
The state government on Friday said Peter Renshaw, executive director of medical services at the hospital, was on extended leave and would retire.
Dr Renshaw worked at the hospital when Griffin was employed.
He told the inquiry in early September he was "unaware" of any marked changes to hospital processes since Griffin's offending came to light.
Chief executive of the hospital, Eric Daniels, who agreed there had been a catastrophic failure of hospital structure and management, will retire in 2023.
The hospital's executive director of nursing, Helen Bryan, is also retiring.
In June, she told the inquiry she could not guarantee every nurse currently employed was fully aware of a mandatory requirement under law to report child sexual abuse suspicions.
The state government is undertaking a governance review of the hospital, while the inquiry is expected to deliver a final report by May.
Premier Jeremy Rockliff said the governance advisory panel determined a dedicated focus on the hospital's senior executive leadership structure was "urgent and essential" to achieve reform.
He said new child safeguarding officers would be recruited and based at the state's four major public hospitals.
