The 49-year-old, who recently split from his partner of 14 years, Vanessa Paradis, is having a hard time riding the horse and producers worry he will hurt himself if he continues to fall, reported Contactmusic.
"It has become a problem for Johnny. He wants to do all his own stunts, but he's been falling off his horse so often that producers worry he's going to do permanently damage his tailbone," a source said.
Depp, who plays Tonto in the upcoming blockbuster, recently said the make-up and appearance for his character was based on a painting by artist Kirby Sattler.
"I'd actually seen a painting by an artist named Kirby Sattler, and looked at the face of this warrior and thought, That's it... The stripes down the face and across the eyes... it seemed to me like you could almost see the separate sections of the individual," he had said.