The man, who is in his fifties, is suspected of handling stolen goods, police attorney Linn Revheim told broadcaster NRK.
He was not present during the break-in at the museum, she said.
“Police found objects at his home,” Revheim told NRK, adding the statements made by the other suspects led to the fourth arrest.
He has been remanded in custody for four weeks, including two in isolation, reports the broadcaster.
University Museum of Bergen institute leader Asbjørn Engevik told NRK that staff “never gave up hope” of seeing the valuable Viking artefacts returned.
The museum is currently working on returning the objects to their previous places while also assessing any damage they may have sustained.
Two-thirds of the objects are now reported to have been recovered.
“It is too early to say how large the damage is, but much can be repaired. The things that are most damaged are the biggest challenge, especially where parts have been broken off,” he said.
Police are assessing whether potential charges against the suspects could include damaging culturally or historically valuable objects.
“We will assess this if and when the charges are brought, in which case potential sentencing would be made stronger,” Revheim told NRK.
The police operation to make the arrest was initiated in October, when a man turned himself in at Bergen Police Station and claimed to have taken part in the robbery, according to the broadcaster’s report.
Police interrogation of the man led to the further arrests in the case.
The man who confessed to police is also under the care of the health service, reports NRK.
The broadcaster also writes that it has received information connecting the two men arrested earlier this week to a drugs-connected group in Bergen.