The star needed surgery to insert a pin in his finger, following an off-set accident in early March.
Producers initially said the injury would cause “minimal” delays, but that has now extended to several weeks.
Around 200 crew have been temporarily stood down until filming resumes.
It is not the first delay to the shoot, which is taking place on Australia’s Gold Coast.
Tropical cyclone Nathan disrupted second unit photography shortly after filming began in February.
Subtitled Dead Men Tell No Tales, the fifth Pirates of the Caribbean film sees Depp reprise his role as the swashbuckling Captain Jack Sparrow.
Javier Bardem plays Captain Brand, a villain described as “a ghost bent on revenge” who holds Sparrow responsible for the death of his brother.
Filming continued on scenes without Depp after his departure on 10 March, but he is now required on set.
Mal Tulloch, from entertainment trade union the Media, Entertainment and Arts Alliance, said his members were not concerned “at this stage” that the production would come to a halt.
“They’ve tried to keep it going in his absence… but they’ve reached the pinch point,” he is quoted as saying.
Although the production still has around 14 weeks of filming left to complete, Disney says the film is still on target to meet its scheduled release date, 7 July 2017.