Ms Heard, married to actor Johnny Depp, had pleaded guilty in court to making a false statement on her immigration.....card about the couple's Yorkshire terriers.
But the Queensland judge gave her a one-month good behaviour bond with no conviction recorded. If she breaks the bond she must pay A$1,000 ($770; £540).
The authorities also released an unusual video apology from the couple.
In the video, which was shown in court and made public by the Department of Agriculture, the couple expressed remorse and advised travellers to respect Australian quarantine laws.