The 72-year-old woman died after suffering Thrombosis with Thrombocytopenia Syndrome (TTS), linked to the AstraZeneca vaccine, SA Premier Steven Marshall confirmed.
She had her first dose of the vaccine on June 24.
"She became unwell and she was admitted to hospital on July 5," Mr Marshall said.
"She has now passed away overnight. Our thoughts are with her family at this very sad time."
The woman was being cared for at the Royal Adelaide Hospital.
"Her death of course has been referred to the TGA as well as to the coroner for further investigation," the premier said.
The death comes as SA enforced an even harder border closure with NSW as cases escalated past 100 today.
Mr Marshall declared Greater Sydney a 'level five zone' of risk from midnight tonight.
The border changes mean South Australians will no longer be able to return to the state unless they get an exemption and undertake 14 days of hotel quarantine.
"We have a serious, deteriorating situation in NSW," SA Premier Steven Marshall said.
SA is on high alert after a man travelled through the state from Greater Sydney while infectious with coronavirus.
The removalist stayed overnight in Victoria on Thursday, June 8 before driving to South Australia on Friday, June 9.
It's believed the man entered the state as an essential worker via the land border.
Contact tracers are now working to establish the man's movements over the past week.
