Duc Nguyen, 43, and a 21-year-old woman appeared by videolink in Melbourne Magistrates Court on Friday.
Their lawyers did not apply for bail.
The pair was charged with murder after a 55-year-old man was shot dead in a Fitzroy street on Tuesday afternoon.
The woman's lawyer Ayla Dodson told the court her client was not accused of being the shooter and her involvement in the offence was "very unknown".
She said her client was withdrawing from drugs and her mental state was rapidly declining as she had not been given anti-psychotic medication since she was arrested on Wednesday.
"She was not in a position to be interviewed due to the nature of her withdrawal issues," Ms Dodson told the court.
Magistrate Graham Keil said he would ensure the woman was given urgent medical attention, medication and psychological assessment.
Homicide Detective Senior Constable Aaron Price said police needed 18 weeks to collate CCTV evidence and transcribe about three hours of audio recordings.
He said it would also take time for police to pull together forensic reports from DNA and ballistic evidence.
Nguyen's lawyer Adrian Lewin said that was too long for his client to sit in jail without knowing the evidence behind his murder charge.
Mr Keil agreed and prosecutors were instead given 10 weeks.
"I'm sympathetic because I do not want people to be lingering in jail," Mr Keil said.
The accused are due back in court on November 4.
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