State public health officials said the man, who died last weekend, was a confirmed case of thrombocytopenia syndrome (TTS).

"On behalf of the Tasmanian government, and personally, I extend my deepest sympathies to the man's family, friends and loved ones," Health Minister Jeremy Rockliff said on Thursday.

The man was vaccinated in a Tasmanian state vaccination clinic.

Tasmanian State Health Commander Kathrine Morgan-Wicks said TTS was a rare but serious condition that affects two in 100,000 Australians who receive a first dose of the AstraZecena vaccine.

Five deaths from TTS have been reported following the administering of 6.1 million AstraZeneca doses. All are linked to people receiving their first dose.

The cause of the man's death will be investigated by the coroner.

"People in this gentleman's age group had been advised to weigh up the risks benefits (of AstraZeneca) carefully for several months certainly before this vaccine was provided," State Public Health Director Mark Veitch said.

"All vaccines carry risks. We're being very frank with people telling them that in this instance someone has had the AstraZeneca vaccine and has developed a serious complication.

"The public does need to know that there are side effects but they also need to know there are benefits from vaccines."

The Therapeutic Goods Administration was also notified of a 48-year-old Victorian woman's death linked to AstraZeneca and TTS in the past week.

Pfizer remains the recommended vaccine for Australians under 60 due to the extremely rare blood clotting condition linked to AstraZeneca.

Ms Morgan-Wicks said people should seek immediate medical attention if they develop symptoms like severe or persistent headaches, blurred vision, confusion or seizures, shortness of breath, chest pain, leg swelling or persistent abdominal pain.

Mr Rockliff said it was normal for people to feel a degree of uncertainty after hearing the news but noted "vaccination is the best way of guarding against COVID-19".

Australian Associated Press