The festival began on Friday and was due to continue until Sunday, but a decision was made by organisers to cancel the remainder of the event after the incident .
“We are working with the emergency services, police and the Health and Safety Executive as they establish the circumstances surrounding today’s incident,” the organisers said.
“We are incredibly grateful to everyone who responded, and to our teams and community for the care they have shown one another.”
Theo Saville, who was at the festival, said a “large wooden sign” had collapsed near the entrance to a tented area.
Sussex Police is urging anyone with information about the incident to contact them.
The Health and Safety Executive and local authority had also been informed, the force added.
The Big Church Festival, which describes itself as the UK’s biggest Christian festival, was founded in 2009.