The tiger at South Lakes Wild Animal Park near Dalton-in-Furness inflicted severe head and neck injuries on Sarah McClay, 24, the BBC reported. She was transported to Royal Preston Hospital.
David Gill, the owner of the park, said he had no idea why McClay entered a tiger enclosure on her own. He described her as "proficient and passionate" about her work.
"We have very strict protocols and procedures for working with big cats, but it seems she failed to follow correct procedures," Gill told BBC Radio 5. "For inexplicable reasons she opened a door and walked into the enclosure. We will never know why she entered without telling anyone. There was no reason for her to go in there."
The attack is being investigated by Cumbria Police.
Gill said the park was closed immediately after the attack. But he said staffers at a meeting a short time later said they wanted to "carry on" and the park would be open Saturday.
The Sumatran tiger poses no hazard to the public and will not be put down, Gill said.
"He didn't do anything wrong. He's a tiger and his natural instinct is to kill," Gill said. "We all know that and that's why all the protocols are in place."
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