South Australia is having a horror start to the 2019 flu season, with the number of confirmed cases already surpassing last year's total.

SA Health says there have been 7500 confirmed cases so far and three people have died.

Health Minister Stephen Wade said the notification rate was "unprecedented" and it is difficult to predict its trajectory as the season progresses.

He urged all South Australians to get a flu shot and said the government had brought forward its free vaccine program.

"People over the age of 65 and children over the age of six months and under the age of five started to receive their flu vaccines in early April," he said.

But the Liberals have been accused of "a dramatic failure in planning" after the Flinders Medical Centre ran out of vaccines for staff.

Mr Wade said the hospital made the decision to bring forward its vaccination program for high-risk areas, and a high percentage of staff took up the early jab.

"In the last three weeks we've had more than 2000 staff vaccinated at the Flinders Medical Centre, of around 7500 staff," he said.

The hospital has now run out of vaccinations for staff, and workers will have to wait until at least next week for their shots.

Opposition health spokesman Chris Picton said the situation put more pressure on an already strained hospital system.

"It's vitally important that our doctors and nurses are protected from the flu," he said.

"If these delays continue, it's more likely doctors and nurses will succumb to the flu, meaning they will have to stay home rather than providing care."