The 26-year-old woman was attacked and killed when she entered the lion’s enclosure, Project Survival founder Dale Anderson said in a statement.
Fresno County police say they found her severely injured, still lying inside the enclosure with the lion nearby.
Deputies shot and killed the animal so they could reach her but she died at the scene, a police spokesman said.
Investigators were trying to determine why the intern was inside the enclosure and what might have provoked the attack, Fresno County Sheriff’s Sgt Greg Collins said.
The facility, known as Project Survival’s Cat Haven, is normally closed on Wednesdays, and only one other worker was present during the mauling.
The 26-year-old woman was not identified by police.
Mr Anderson was crying as he read statement to reporters on Wednesday, saying the group would investigate if their protocols were followed before the attack.
The lion was a four-year-old male named Couscous, a California Fish and Wildlife spokesman said.
Couscous had been raised at Cat Haven since he was eight weeks old, said Tanya Osegueda, a spokeswoman for Project Survival.
Lt Tony Spada of Fish and Wildlife told the Fresno Bee this type of incident was “very rare” because of the safety measures required by the state and because regulations require minimal human-animal interaction.
“This facility has a very good history,” Lt Spada said. “In this case, someone just got too close.”
Cat Haven is about 45 miles (75km) east of Fresno.
The project opened in 1993, and has housed numerous big cats, including Bengal tigers, Siberian lynx, jaguars and leopards.