Detectives from the missing persons squad arrested the man, who is not linked to the Murphy family, at his Ballarat home about 6am on Wednesday.
On Thursday afternoon they charged him with murder and he will face Ballarat Magistrates Court.
Police are yet to find Ms Murphy's body and the investigation is ongoing.
Shortly before police announced the charges, Ms Murphy's husband Michael told reporters charges had been laid over his wife's disappearance.
He did not go into further details.
Ms Murphy, a mother of three, left her home at Eureka Street in Ballarat East on February 4 to go jogging and has not been seen since
"Despite a significant investigation and extensive searches of the Canadian Forest area, no trace of the 51-year-old has been located," police said in a statement on Thursday.
"There are no further updates at this time and the investigation remains ongoing."
No trace of the 51-year-old has been found since her disappearance on February 4. (James Ross/AAP PHOTOS)
Officers have spoken to a number of people as part of their investigation into Ms Murphy's disappearance, police said.
In late February, Detective Acting Superintendent Mark Hatt said it was most likely her disappearance involved one or more parties.
Police were doubtful she was still alive and had been looking at the possibility her body was moved from where she vanished, Det Supt Hatt told reporters on February 23.
Anyone who has information about Ms Murphy's disappearance, including CCTV or dash-cam footage from the time she went missing, is urged to come forward.
"We understand that there is a continued high level of interest in this investigation and concern about Samantha's disappearance, however it remains critical that any speculation does not impede any aspects of the investigation," a police spokeswoman said on Thursday.
Husband Michael Murphy and the couple's daughter Jess had appealed for public help to find her. (James Ross/AAP PHOTOS)
Ms Murphy's disappearance sparked weeks of extensive searches around greater Ballarat area by trained emergency services workers and hundreds of concerned locals.Â
They combed through dense forest, private land and walking tracks.
Buninyong Police Station, which was originally a base for the search operation for Ms Murphy, was unattended on Thursday with the lights off and door closed.
A whiteboard with a map showing where the public could help search was long gone, and a sign on the door instructed anyone with information to contact Crime Stoppers.
Ms Murphy has been described as mentally and physically fit and was training for an upcoming race by doing 15km runs.
Detectives have been working with telecommunications technicians to track the route she travelled, after confirming she had a smartwatch and phone on her.
Ms Murphy and her husband Michael run a car repair business called Inland Motor Body Works at Delacombe, a few suburbs from their home.
News crews staked out the Murphy household near Eureka Street on Thursday, where Mr Murphy was seen walking into his shed before getting into his truck and driving away.
He told AAP police had advised him not to comment to the media at this stage.
Mr Murphy and the couple's eldest daughter Jess previously issued a public plea to help find her.
"Mum, we love you so much and we miss you, and we need you at home with us," Jess told reporters on February 8 in Ballarat.
Police in Victoria can only hold people in custody after an arrest for a reasonable time before they issue charges, however the law does not state what a reasonable time is.
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