Heard, 29, had been ordered to appear in an Australian court on Monday on charges of failing to declare her terrier dogs to Customs officials.
She failed to appear but the case has now been adjourned until November 2, reported BBC.
The actress faces a possible 10-year jail term or a hefty fine for illegally importing the dogs into Australia and of producing a false document.
The discovery of the dogs in a Gold Coast mansion where the couple were staying earlier this year sparked a public spat with Australia's Agriculture Minister, attracted international media attention and was dubbed the #WarOnTerrier by social media.
Australia has strict quarantine laws to prevent diseases being imported into the island nation.
Heard was spotted over the weekend supporting her husband at the Venice Film Festival.
The Yorkshire terriers were flown from Australia unharmed The dogs, Boo and Pistol, are understood to have arrived in Australia on board Depp's private jet in April this year.
The star was in Australia filming the fifth movie in the Pirates of the Caribbean franchise on Australia's Gold Coast.
The dogs were discovered when a picture was posted of them at a grooming parlour.
Joyce said he didn't care if Depp had been voted the "sexiest man alive", he still had to adhere to quarantine rules.
The dogs left the country unharmed a few days later.
Depp recently took aim at Joyce at a press conference in Venice.
"I killed my dogs and ate them under direct orders from some kind of, I don't know, sweaty, big-gutted man from Australia," Depp said.
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