Marissa Dub, believed to be about 21, was airlifted to Indianapolis after the mauling, The Indianapolis Star reported.
Dub was cleaning the tiger's cage at the Exotic Feline Rescue Center in Center Point when the tiger bit her head, Rob Gambill, chief deputy sheriff for Clay County, said. He said workers had moved the tiger into another area, but the sliding door failed to shut completely.
"This is such a sad deal," Gambill said. "This poor girl."
Other workers at the center used meat to distract the tiger and a fire hose to encourage it to move away, Gambill said.
The center has about 230 exotic cats, including tigers and lions. It provides a home for animals that have been mistreated or abandoned.