"Just because he's Johnny Depp doesn't make him exempt from Australian laws," Mr Joyce said.
"The way this works is if we are going to make an excuse for Johnny Depp because he's got a private jet and brought in his dogs then I suppose you have to start making exemptions and excuses for everybody.
"The reason you can walk through a park in Brisbane and not have in the back of your mind 'what happens if a rabid dog comes out and bites me or bites my kid' is because we've kept that disease out.
"I'll tell you how close it is: it's in Bali, it's just next door. So this is not fanciful stuff, and therefore we're very diligent about what comes into our nation."
When Mr Joyce was asked if his tough stance might affect Depp's view of him, he replied: "I don't think Mr Depp will be inviting me to the grand opening of the Pirates of the Caribbean."
A US embassy spokeswoman said it encouraged US residents to do their research before travelling abroad.
"The US Department of State advises American citizens travelling to Australia that Australian customs authorities enforce very strict regulations concerning the importation from all countries of items such as agricultural and wood products, as well as very strict quarantine standards for other products, animals, and pets," the spokeswoman said.
"We advise travellers to contact the Embassy of Australia in Washington, DC, or one of Australia's consulates in the United States for specific information regarding customs requirements, and visit the Australian Government's Department of Agriculture website."
Totally agree with Mr Joyce.