More than 700,000 South Australians have had a flu vaccine this year with a program of free jabs boosting numbers in recent weeks.

The state government is offering free flu vaccinations to anyone during June amid fears COVID-19 infections and rising influenza cases could further stretch hospital resources over winter.

So far 721,643 people or 41 per cent of the eligible population have had a flu jab, including 146,114 during the first two weeks this month.

Health Minister Chris Picton said this winter was expected to be severe in terms of both coronavirus and influenza cases.

"Our hospitals are already under extreme pressure with COVID-19, flu and normal winter demand," he said.

"You don't want to end up in hospital this winter. And you don't want to put vulnerable family members at risk.

"Let's all work to protect our doctors, nurses and hospital staff, and protect our hospital system."

The take-up rate for flu jabs has been strongest among South Australians aged over 65 with 270,949 or 77 per cent inoculated so far.

Across SA, the number of people who have had three doses of the COVID-19 vaccine sits at about 73 per cent of those eligible, or more than 985,000.