It comes as campaigners have warned that a record 250 free-to-use cash points are closing each month.
The supermarket says it's trialling the removal of cashback at the majority of its stores that have free cash points in the vicinity.
The Sun has asked Sainsbury's to confirm how many stores this affects and how long the trial is expected to last – we'll update this story as soon as we get a response.
Sainsbury's says the idea behind the trial is to prevent the duplication of services but many shoppers are unhappy about the decision.
Some say they don't feel safe using ATMs to withdraw cash outside stores.
One Twitter said they were "disappointed" by the decision, writing: "Disappointing to hear my local store is stopping cashback.
"What about the elderly who fear using cash machines who get cash back instead. What about busy working people who are short on time who get cashback to save them time? Where did customer service go?"
Another wrote that it’s "dark, cold and potentially dangerous to ask your consumers to stand outside and withdraw money".
It's not just safety that shoppers are worried about, some point out that getting cash from the checkout when making a purchase is simply quicker and easier than having to go to the ATM before or after their shop.
One Twitter user wrote: "It is very inconvenient to not be able to get cashback at your tills. Please go back to doing it. I don't feel safe using ATMs outside."
Another shopper reported the trial resulted in miscommunication when he wanted to withdraw money in store.
"Today I went to the checkout, then to the cash machine then back to the checkout… hope the trial results in the facility being reinstated."
Consumer group Which? has recently urged the financial regulator to "urgently intervene" to stop further ATM closures and ensure that no more consumers are suddenly stripped of their access to cash.
In the summer, LINK cut the fees operators receive from banks for ATM cash withdrawals.
Campaigners fear that the move could lead to closures in rural communities or a rise in pay-to-use ATMs.
Earlier this year Which? estimated that 300 cash machines a month were closing across the country.
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