Visitors are putting themselves at risk by getting too close to deer, park officials say.
Wollaton Park in Nottingham allows its two deer herds to roam free.
Numerous signs warn visitors to keep their distance, especially during the current rutting season when the animals can be especially aggressive.
But one family was seen allowing a boy to approach a stag, apparently for a photograph, an action described as "disappointing" by park authorities.
The 500-acre park has two herds, 90 red deer and 120 fallow deer.
Witness Carole Wilson said: "It is very common, you even see people trying to take selfies and getting too close to the deer.
"It's crazy. These animals probably weigh close to one tonne and they have a set of daggers on the top of their heads.
"My husband challenged them, explained the dangers and they said 'Oh really?', they seemed really surprised."
Mrs Wilson added she feared if somebody got hurt, the deer might have to be moved.
Dave Trimble, Nottingham City Council's member for leisure and culture, said: "Most people who visit Wollaton Hall and Park sensibly enjoy our beautiful deer from a distance and observe the many signs around the park advising of the risks to themselves and the animals in getting too close.
"It's disappointing that there are still some people who choose to ignore the signs or apply common sense, risking injury and unsettling the deer."
The council also emphasised dogs should be kept under control with a fine of up to £1,000 possible for anyone worrying the deer.