The Scotsburn man, who cannot be named for legal reasons, was arrested about 6am on Wednesday at his home.
He was charged with murder on Thursday afternoon, more than a month after Ms Murphy, 51, went missing from her Ballarat East home to go jogging.
The man faced a packed Ballarat Magistrates Court about 3.40pm on Thursday, where his lawyer David Tamanika applied to have his name and other details suppressed from media reporting.
Mr Tamanika said releasing the name could cause prejudice to his client, who had been suffering from poor mental health since he was arrested.
Magistrate Michelle Mykytowycz granted the temporary suppression, after several media outlets stood up in court to object.
Prosecutors asked for 20 weeks to compile evidence to hand to the defence, due to there being "a significant amount of material" that needed to be analysed.
The man was taken back into custody and will next face court on August 8.
Police say Ms Murphy, a mother of three, left her home at Eureka Street on February 4 to go jogging and has not been seen since.
Her body has not yet been found.
The police investigation continues and anyone with information about Ms Murphy's disappearance, including video footage, is urged to come forward.
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