According to The Local Democracy Reporting Service the council’s policy follows independent legal advice which found legislation around this subject could be interpreted in different ways, which led some other authorities to allow mobile premises.
It said fixed premises gave practitioners and regulators greater control over infection prevention, hygiene and waste management.
The treatments could be invasive and carried a risk of blood-borne viruses and other infections if appropriate safety measures were not followed, the council said.
Follow BBC Devon on X, external, Facebook, external and Instagram, external. Send your story ideas to spotlight@bbc.co.uk, external.