Ten crews from Devon and Somerset Fire and Rescue service tackled the blaze at a temporary building which was extinguished after 30 minutes.
EDF Energy said construction work had not been affected and an investigation into the cause was under way.
A company spokesman told the BBC it was a “small fire in a temporary building away from the main construction area”.
Hinkley Point C is being built by main contractor Bouygues/Laing O’Rourke Joint Venture (BYLOR) and is expected to open in 2026.