The free vaccines were introduced at the beginning of the month in a bid to increase the number of people immunised as more influenza cases emerged.
Health authorities feared rising infections at the same time as persistently high COVID-19 cases, would put increasing pressure on the state's already stretched public hospitals.
Coronavirus cases are also expected to surge in coming weeks following the arrival in SA of the BA.4/BA.5 Omicrone variant.
Opposition health spokeswoman Ashton Hurn says now is not the time to stop the free flu jabs.
"Right now, our hospitals are overflowing and the government should be doing everything it can to ease the pressure" Ms Hurn said.
"Vaccination is the best way to protect yourself from the flu, so the last thing we need this winter are any barriers keeping South Australians from getting this potentially life-saving vaccine.
"We need every line of defence up and running over the coming months and failing to extend the free flu program is a huge gamble."
But Premier Peter Malinauskas said the government's decision to offer free vaccines for a month was designed to encourage people to take them up as quickly as possible.
He said that had resulted in a substantial increase in the number of people vaccinated.
"By putting a timeline on it, it was all about encouraging people to get that vaccine as quickly as they possibly can," he said.
"We were very clear about that timeline.
"As it currently stands, if South Australians want to get the vaccine for free, they should be doing it as quickly as they can."
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