Karmelle Pelham, 39, from Worksop, had been enjoying a family day out when park staff told them the site was being evacuated.
She said she had heard what sounded like “gunshots” and an air ambulance had circled above.
Pelham added: “There was a big, black tarpaulin over the tiger enclosure.”
She praised park staff for their handling of the incident, saying it had been “very, very well organised”.
Foreign Secretary and MP for Doncaster North Ed Miliband said he was “deeply saddened” to hear of the incident and sent his “thoughts and deepest condolences to the family of the individual who died.”
He added he was “very grateful to the emergency services and staff of the park who responded.”
Lee Pitcher, MP for Doncaster East and the Isle of Axholme, expressed his gratitude to emergency services for their response.
In a statement shared to social media, he said he was “deeply saddened to hear about the tragic incident that has taken place at Yorkshire Wildlife Park today”.
Yorkshire Wildlife Park opened in 2009, with its Land of the Tigers area opening in 2011.
The purpose-built two-acre reserve is home to Amur tigers, an endangered subspecies with around 500 left in the wild.
Photos of the enclosure on the park’s website shows a high walkway for visitors and fencing above the section where the tigers can roam.
Additional reporting by James Kelly