The 53-year-old actor was issued with a temporary restraining order following claims that he was "verbally and physically abusive" to Heard, 30, throughout their four-year relationship.
A spokeswoman for Los Angeles Superior Court said the case - which had been due to be heard today - will now take place on 15 and 16 August.
The move comes after a telephone discussion between the judge and lawyers for Depp and Heard on Thursday.
Attorney Christopher Melcher, who previously served as chair of the state bar of California family law section, said the delay allows Depp to gather more witnesses to defend himself against abuse allegations, while for Heard it allows the restraining order to remain in effect at least until the next hearing.
There have been conflicting media reports about whether the two sides are moving toward a settlement in the divorce case.
Heard filed for divorce, citing irreconcilable differences, on 23 May - just days after the death of Depp's mother, Betty Sue.
In papers filed with the court, Heard said Depp had a "history of drug and alcohol abuse" and she lives "in fear" of him.
Last month, she submitted photographs to the court appearing to show her bruised face, which she said was a result of Depp hurling a mobile phone at her on 21 May.
On 27 May, a judge granted a temporary restraining order for Depp to stay at least 100 yards away from Heard.
In a counter argument, Depp's lawyer said in court papers that Heard "is attempting to secure a premature financial resolution by alleging abuse".