Depp, 54, now sports a mohawk haircut for his European tour with his rock and roll tribute band, Hollywood Vampires, and lacks his trademark tan, long hair, moustache and beard, which he wore for his character of Jack Sparrow. Some fans don't approve of the new image.
"Please grow some hair on your head and face, and get suntanned," posted one Instagrammer.
Others posted comments saying that Depp's undercut hairstyle made him look like a cancer patient. But diehard fans defended the star's appearance. "I like his hair β¦ He looks happy," posted @carriecafe.
"He looks like this for a new movie[,] he is fine and not sick," posted @astridinfrance.
Comments on Instagram also raised the possibility that that this is what Depp looks like without his trademark Pirates of the Caribbean makeup.
Another Intagrammer even suggested that he might be high.
Depp has been nominated for three Academy Awards since his career launched in 1984.
He has been married twice, most recently to the actor Amber Heard who alleged that Depp was physically abusive.
The couple divorced acrimoniously in 2016 and are estranged.
Depp had a long-term partnership with French actress Vanessa Paradis and they have two children together.
When he's not acting in Hollywood movies, Depp tours the world with Hollywood Vampires, the supergroup he formed with Alice Cooper as a tribute band to rock stars who have died prematurely.
But Depp's fans sincerely hope that he is not planning on joining the dearly departed any time soon.
"[Y]ou need to be eating more, sir, you are looking a little thin," wrote @wickedwolfink. "We don't want to lose you."
"I think that my hero looks ill," one admirer posted on Twitter.
But since Depp turns 55 on June 9, perhaps he's just looking his age.