The blaze destroyed about 1,000 sq m of scrubland at Bradgate Park, in Newtown Linford, Leicestershire, at about 16:45 BST on Saturday.
Bradgate Park Trust said a cigarette or an illicit barbecue within the park's grounds could have been to blame.
The trust said it was a "sad day" and reminded visitors of the "devastation" a fire can cause.
Marc Rose, who was visiting at the time, said he saw "thick, black smoke" as he walked near the reservoir.
The 28-year-old, who was enjoying temperatures of 20C at the attraction with his family, said: "We could see firefighters and park rangers using what looked like snow shovels to dig out the heather and bracken, which had caught fire.
"The park was very busy at the time and the fire was quite close to the main path, where a large crowd had gathered and many people were taking photographs."
The trust wrote on Twitter: "A reminder of the devastation fire can cause.
"We don't know if it was a BBQ or cigarette butt - the result is the same."
Peter Tyldesley, director of the trust, said: "The fire was within an area of bracken litter, which is incredibly flammable - like a tinderbox.
"Barbeques are not permitted anywhere within the country park or car parks.
"In a dry summer, the park and its wildlife could be devastated by one carelessly dropped match or cigarette end.
"We expect all visitors to be alert to the risk of fire from their actions."
Mr Tyldesley thanked Leicestershire Fire and Rescue Service and "all who were involved in helping to control the blaze" at the country park.
The fire service recorded the incident as "deliberate", but does not believe it was arson.
A discarded cigarette butt could have caused a fire which "devastated" a country park, its owners have said.