The owners of the Lee Meadow Campsite, near Woolacombe, closed the site after a visit by environmental health officers.
North Devon Council would not say how many people had fallen ill, but one holidaymaker told the Journal he believed as many as 150 people may have been affected.
The man, who stayed at the campsite last week, said: "Almost every tent on the site was affected. There were so many sick children — it was an awful sight to witness.
"At night all you could hear was vomiting from every corner. I've never experienced anything like it.
"People were simply zipping up their tents and leaving — they just wanted to get out of there.
"Who knows how many people went home without knowing what they were carrying?"
In a statement North Devon Council said: "We have been working with the Health Protection Agency and the NHS to investigate reports of a number of people suffering from sickness and diarrhoea.
"Environmental health visited the site, took samples from the water supply and stool samples from campers.
"The nature of the illness is not yet known but the HPA and medical advisors at North Devon District Hospital suspect Norovirus."
The council said the owners took the decision to close the campsite.
The site has a private water supply which has been closed off due to possible contamination.
South West Water brought water supplies onto the campsite after learning of the illness.
A spokesman for the water company said: "Lee Meadow Farm has its own private supply from a borehole and is not connected to our mains water supply.
"When the private supply became unavailable due to possible contamination, we provided Bowsers and arranged water deliveries to the site.
"We are now discussing with the owners the possibility of connecting directly to the mains supply. However this is not a simple matter as we have to be sure there is no risk of contaminating the public supply from another source."
The owners of the site did not wish to speak to the Journal about the outbreak.
It's understood the campsite opened for the first time last year.
Last year it received positive reviews on a camping website from people who praised its facilities and friendly welcome.
Norovirus can be transmitted by contact with an infected person, by consuming contaminated food or water or by contact with contaminated surfaces or objects.
Symptoms, which will last for 12 to 60 hours, include vomiting and watery diarrhoea.
The council's investigation into the outbreak is continuing.