The actor, who is currently Down Under filming his fifth "Pirates of the Caribbean" film, is accused of smuggling in his Yorkshire terriers, Pistol and Boo, because he allegedly didn't have the proper documentation for the dogs when his private jet, which carried the pooches, arrived in Queensland in April, several reports said.
This is the second major hiccup that Depp has faced while filming "Pirates 5." The actor left the country for the United States in March to get surgery after he injured himself on a glass door. It was on his return flight to Australia that he reportedly didn't declare wife
The 51-year-old could face a $60,000 fine or 10 years in jail, according to CNN's Kendall Gilding. That's in addition to the threat of euthanasia for the animals.
The country has strict biosecurity laws, which require certification and permits to prevent the spread of non-native diseases. The pups were required by law to spend 10 days in a government quarantine facility upon arrival in Australia, reports said.
On Thursday, Minister of Agriculture Barnaby Joyce called the actor out, saying on TV that if Depp didn't "take his dogs back to California," they would be euthanized. The "Mortdecai" star has until Saturday in Australia to meet the 72-hour ultimatum.
"Basically it looked like he snuck them in," Joyce said, before going on a tirade about not giving the star special treatment.
"If we start letting movie stars, even if they've been 'Sexiest Man Alive' twice, to come into our nation then why don't we just break the laws for everybody," he said (via the Associated Press). "It's time that Pistol and Boo buggered off back to the United States. After that I don't expect to be invited to the opening of 'Pirates of the Caribbean.'"
After the alleged smuggling, Depp's assistant reportedly took his wife's furry friends to a groomer in Maudsland, Joyce said. The groomer, Happy Dogz, posted an article about the couple and their pets on its Facebook page, saying it was "an honor to be grooming Johnny Depp and Amber Heard's two Yorkshire Terriers." That might have been what tipped off authorities.
Pistol and Boo are currently under house quarantine in the Gold Coast mansion where Depp is staying, CNN said.
The fracas has fomented outrage online and given rise to a Change.org petition to save the dogs. The petition had so far received more than 15,000 signatures.
Depp's publicist and attorney did not immediately respond to requests for comment.