Missing persons squad detectives arrested the 22-year-old from Ballarat at his home about 6am on Wednesday, Victoria Police said.
He is yet to be charged as of Thursday morning.
Police say he is not linked to the Murphy family.
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.”
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.
Murphy’s disappearance sparked weeks of extensive searches around greater Ballarat area by trained emergency services workers and hundreds of concerned locals.
They combed through dense forest, private land and walking tracks.
She 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.
Murphy and her husband Michael run a car repair business called Inland Motor Body Works at Delacombe, a few suburbs from their home.
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.
– AAP
