They were given the opportunity to re-book the following day, when an extra clinic was organised.
The problem centred around an error in the temperature readings of a vaccine fridge on Thursday.
A spokesperson for the clinic told the BBC: "The clinics were postponed as a precautionary measure as patient safety is of the utmost importance."
A Somerset Clinical Commissioning Group spokesperson told the broadcaster all vaccine fridges are "closely monitored".
They added: "We can confirm that an error was found on the temperature reading of the vaccine fridge...which resulted in an alarm being triggered.
"It's extremely important that vaccines are stored at the correct temperature to ensure that they will work properly."