South Yorkshire Police said they were called at 13:35 BST on Saturday to reports of a man entering the tiger enclosure at the park. The force confirmed the tiger "attacked the man and this has resulted in serious injury." Officers were attempting to contact the man's family.
In a statement on its website, the park said its emergency response procedures had been "immediately activated" and it was "working closely with the authorities to ascertain exactly what happened." The park will remain closed for the remainder of the weekend.
The tiger remained inside the enclosure following the incident, and police said there was "no wider risk to the public." The park was evacuated and officers remain at the scene. Police have urged people not to share "distressing footage" of the incident.
Yorkshire Ambulance Service said it had deployed an air ambulance, two land ambulances and a doctor.
The park said the safety and wellbeing of its visitors, staff and animals "remain our highest priority."
Yorkshire Wildlife Park opened in April 2009, and its tiger enclosure, known as Land of the Tigers, opened in 2011. The park describes the area as one where the big cats can roam woodlands and grasslands or play in a waterfall pool. Its other animals include lions, leopards, cheetahs, polar bears, brown bears and sea lions.