Energy firm Cuadrilla started construction work at the site at Preston New Road, Little Plumpton, Lancashire, in January.
Five men and a woman were arrested on suspicion of offences under the Public Order Act, Lancashire Police said.
The men, aged between 23 and 55 from Blackpool, and a 51-year-old woman are being questioned in police custody.
Another man, 53, has been reported for summons.
What is fracking and why is it controversial?
Fracking is the process of drilling down into the earth before a high-pressure water mixture is directed at the rock to release the gas inside. Water, sand and chemicals are injected into the rock at high pressure which allows the gas to flow out to the head of the well.
The government approved energy firm Cuadrilla's plans to frack at the site in October.
Protests have been held at the site since work started on 5 January.
Cuadrilla has previously said drilling would start in the spring.
A second Lancashire site, Roseacre Wood, has not yet been given permission to operate amid concerns over the impact on the area.
The council had initially refused permission to extract shale gas at both sites on the grounds of noise and traffic impact but the government overruled the decision for the Preston New Road site.
Six anti-fracking protesters have been arrested near to the UK's first horizontal fracking site.