Health officials say there's been two cases of blood clots linked to the AstraZeneca vaccine in South Australia, including a 53-year-old man in intensive care.

A 53-year-old man is in a serious condition in intensive care in Adelaide after being confirmed with blood clots linked to receiving the AstraZeneca COVID-19 vaccine.

SA Health says the case of thrombosis with thrombocytopenia syndrome (TTS) was confirmed late on Wednesday and is the first confirmed case in SA.

It says officials have also been made aware of another probable case in an 87-year-old woman who is in a stable condition in hospital.

The two SA cases are among six confirmed or probable new cases across the country in the past week, according to the Therapeutic Goods Administration.

Chief Public Health Officer Nicola Spurrier said the man had his first dose of the vaccine on May 4 and was admitted to hospital on May 18 with severe abdominal pain.

"We were made aware of this case and the clinicians involved were very quick to get the information to the TGA," Professor Spurrier said.

"It is a rare occurrence but because of the number of vaccines that we're giving across our whole community it was not unexpected for this to occur."

Professor Spurrier said given about 150,000 doses of the AstraZeneca vaccines had been administered in SA so far, the one confirmed case of blood clots was within the expected range of about one in 100,000.

She said SA would continue to follow the health advice from national officials on the administration of the vaccine.

"I'm a pediatrician and public health physician. I'm not an immunologist and I'm not a vaccine expert, so that's why we have a group where those experts come together to provide this advice for our community," Professor Spurrier said.

"People need to think about this one in 100,000 risk. There are risks to everything we do in life and there are certainly risks to all medications.

"But we are still not out of the woods with COVID-19 and vaccines continue to be the best way of protecting yourself from an infectious disease."

Professor Spurrier said all South Australians would hope the man in ICU made a speedy recovery.

SA also reported one new COVID-19 case on Thursday in a woman in her 30s who recently returned to Australia from overseas.

The state currently has seven active infections, all returned travellers in hotel quarantine.