Officials at Salt Lake City's Hogle Zoo said the leopard, Zeya, was spotted around 9:30 a.m. outside her enclosure in the Asian cats exhibit.
Zoo spokeswoman Erica Hansen told the Salt Lake Tribune that Zeya was found sleeping on a wooden beam a foot or two outside her enclosure. The leopard wasn't acting aggressive but appeared to be snoozing.
She woke up briefly when she was hit with the tranquilizer dart, but fell back to sleep.
Zeya has lived at Hogle Zoo since last October, according to officials. She came to Utah from the Wildlife Heritage Foundation Big Cat Sanctuary in England.
The incident quickly spawned a parody account on Twitter.