Depp reportedly walked off the set of Pirates of the Caribbean: Dead Men Tell No Tales in Queensland on Wednesday night, according to the Gold Coast Bulletin.
The actor was meant to be shooting scenes as the swashbuckling Captain Jack Sparrow on the Gold Coast but it was reported he planned to return to Los Angeles as soon as he could to be with Heard.
It would have been another major set back for the Disney production, which is already behind schedule after Depp, 51, suffered a hand injury in March.
Johnny Depp with Pistol the terrier, who was deported from Australia last week.
Heard, an actress and model, left Australia with the couple's undeclared pet dogs last week after Yorkshire terriers Pistol and Boo were told to leave the country or be put down.
Depp was originally planning to jet off with Heard and the pooches but changed his mind after producers stepped in and convinced him to stay.
The couple's marriage is said to be shaky, with Heard's close friendship with photographer and gay activist Io Tillett Wright causing bickering.
Some US entertainment sites claim Heard had previously been asked to leave the Pirates set by producers because the couple's constant fighting was causing disruptions.
Heard, 29, married Depp on his private island in the Bahamas in February and is openly bisexual.
Depp injured his hand while with friends in Australia in March and departed to the US for surgery.
He was initially expected to return two weeks later but the break extended for more than a month, with almost half the 400-strong crew temporarily stood down.
Script issues and Tropical Cyclone Nathan have previously hampered production of the film, and the original $250 million budget has been significantly blown out.
