The accused was being questioned by police on Monday afternoon.
“We are uncertain whether he has anything to do with the murder case; he was arrested in connection with another case involving a domestic dispute,” said police prosecutor Asbjørn Onarheim.
He added that the suspect lived in the area and was known to the police. He was not related to the victim.
Police said the suspect was intoxicated, aggressive and injured at the time of his arrest.
A home-help nurse alerted the police at 9.37pm after entering Feste's apartment and finding her dead body in the vicinity of the bedroom. The victim had suffered severe head injuries, newspaper Bergens Tidende reports.
According to initial witness reports, a man was spotted in the apartment shortly before the victim's body was discovered.
There was no sign of forced entry at the council-owned apartment in the Oshaugen district where Feste had lived for at least seven years, the newspaper said.