Al Jazeera correspondent in Norway said that the shooting took place inside the mosque "Center for Islamic light" on the outskirts of the capital Oslo.
Police said on Twitter that the shooting took place inside the center, which includes the mosque in the town of Bayram.
She added that she had arrested a suspect, "European" ruled out that there are others involved in the shooting.
Police imposed a security cordon, finding a weapon inside the mosque and arresting one person.
Police cordoned off mosque and arrested one person (Reuters)
The imam, Irfan Mushtaq, told local media the bomber, a white man, was armed with several weapons.
"He appears to be a Norwegian who entered the mosque and was armed with a rifle and pistols," he said. He said the victim was a 75-year-old worshiper.
According to the channel "NRK" public that police found several weapons inside the mosque, and managed to a person in the place to control the attacker before the arrival of security forces.
Al-Jazeera's correspondent said the motives for the shooting were not yet known and that investigations were underway.
Earlier this year, the mosque took more security measures after a massacre by a white extremist inside two New Zealand mosques that killed more than 50 Muslims.