The attack took place on the eve of the Muslim celebration of Eid Al-Adha, marking the end of the Muslim pilgrimage Hajj, and police said they were looking into whether any steps needed to be taken to "improve security".
The man suspected of a shooting at a mosque in Norway may also have killed a relative before launching the attack, police said late on Saturday.
"A young woman was found dead at the suspect's address," assistant chief of police Rune Skjold told a news conference, adding that the man was suspected of murder.
Police earlier said a "young white man" had been apprehended following an armed attack at the al-Noor Islamic Centre near the country's capital, adding that members of the congregation had overpowered the gunman and stopped the shooting.
An older man sustained light injuries in the attack but it was too early to say if the wounds were caused by the gunshots or sustained during the attempt to restrain the gunman, according to police.
An initial statement had said one person was shot in the attack.
The suspected attacker appeared to have acted alone, the police added.
"He is around 20 years old, a Norwegian citizen from the area," Skjold told Reuters.
Only three people were present in the mosque at the time of the attack, preparing for Sunday's celebration of the Eid-al-Adha festival, which up to 1,000 people had been expected to attend, mosque spokesman Waheed Ahmed told Reuters.
The mosque earlier this year implemented extra security measures following the massacre of more than 50 people at two New Zealand mosques by a suspected right-wing extremist.
'Blood on the carpets'
"One of our members has been shot by a white man with a helmet and uniform," Irfan Mushtaq, head of the mosque, told local newspaper Budstikka.
Mushtaq told another Norwegian newspaper, VG, that the man had carried multiple weapons, but that he had been subdued by a member of the mosque.
Mushtaq said he had arrived at the scene shortly after being alerted about the gunman, and had gone to the back of the building while waiting for police to arrive.
"Then I see that there are cartridges scattered and blood on the carpets, and I see one of our members is sitting on the perpetrator, covered in blood," Mushtaq told VG.
He said the man who apparently overpowered the shooter was 75 years old and had been reading the Koran after a prayer session.
According to Mushtaq, the mosque had not received any threats ahead of the shooting.
The Norwegian Police Security Service (PST) said it was monitoring the situation.
"We're following the events and are continuingly evaluating. It's to early to draw any conclusions," Martin Bernsen, information director at PST, told public broadcaster NRK.
White nationalist attacks
There has been recent spate of white nationalist attacks in the West, including in the United States and in New Zealand where 51 Muslim worshippers were killed in March in shootings at two mosques in the city of Christchurch.
The al Noor Islamic centre in Norway shares its name with the worst affected mosque in the New Zealand attacks.
Budstikka said it had contacted the mosque in March after the Christchurch massacre and that officials there had said security would be tightened.
The suspect in the Christchurch killings wrote a hate-filled manifesto in which he said he was influenced by far-right ideologues including the Norwegian mass murderer Breivik.
Breivik, who said he was motivated by his hatred of multiculturalism, detonated a massive bomb in Oslo that killed eight people and then opened fire on a gathering of the Labour Party's youth wing on the island of Utoya, killing another 69 people, most of them teenagers.