Johnny Depp -- Dogs Kill Sheep, So Get Your Yorkies Out of Australia, or Else

Johnny Depp's 2 tiny dogs are capable of wreaking havoc in the Australian animal kingdom, and that's why the dogs now have a target on their adorable heads.

The Minister for Agriculture, Barnaby Joyce, tells TMZ, Johnny and Amber Heard are not giving due respect to the enormous problem the country faces with animals. Joyce says wild dogs kill up to 40 sheep a night ... though we're guessing none of the offenders are Yorkies.

But size doesn't matter, because Joyce adds they have a real interest in making sure dogs that come into the country are free of disease so Australians can walk their pooches with confidence they won't get sick.

As we reported, Johnny and Amber apparently smuggled Boo and Pistol into the country without the proper quarantine and now authorities say if the dogs aren't out of the country by Saturday, they'll be destroyed.