The society said the exposure to radiation from CT scans was not made clear to consumers in the promotion.
Tesco partner Lifescan is offering the CT scans as part of a 'health MOT'. The deal gives Tesco ClubCard holders £40 of Lifescan vouchers in exchange for £10 of Tesco vouchers.
The SOR said Lifescan was a reputable company, however the body has voiced doubts in the past over the benefits of running CT scans on healthy people.
SOR chief executive Richard Evans said the scans could increase the number of worried well by uncovering abnormalities that were benign.
In response, Tesco told the BBC that Lifescan employed qualified staff who explained the risks to consumers.
Other third-party companies to tie up with Tesco ClubCard include SK:n, a cosmetic skin clinic, and laser eye-treatment specialist Optimax.