EDF Energy brought the action against the group, which has occupied a farm building on the site since February 12.
Protesters were angry that EDF has been allowed to carry out preparatory work before planning permission was granted.
A further injunction to stop any future protests has been rejected.
An EDF spokesperson told the BBC: “EDF Energy is pleased with the decision of the Court to grant both the possession order and injunction order in relation to the people currently camping on ground at the proposed Hinkley C construction site.
“This is a sensible decision which will allow us to proceed with our development for what we hope will be the first new nuclear power station in the UK for more than 20 years.”
Protester Nikki Clark said “We’ve drawn attention to what’s going on there – and they were trying to get a ban on all future protests against nuclear and they didn’t get that so of course it’s a victory.”