"The man will be questioned as soon as possible, and a decision on remanding him in custody is expected later this week," violent crime unit head Egil Kulseth said in a statement, adding that he did not rule out further arrests.
Police said the man, aged around 30, was being questioned on suspicion of being either the perpetrator or an accomplice in the attempted murder.
Nehma Ali Shah, the imam of the Central Jamaat Ahle-Sunnat mosque, was attacked with a "sharp object" by a masked assailant close to his home on June 17.
According to Norwegian online newspaper Nettavisen, Shah left hospital after two days and has not dared go to the mosque since the attack.
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Several Norwegian media outlets have reported on a power struggle within the mosque, which has a congregation of more than 5,000 members mainly of Pakistani origin.
In 2006, several men attacked worshippers at the mosque during prayer time, injuring four.
Shah has repeatedly condemned religious extremists, and made a 2006 visit to the Oslo Synagogue after shots had been fired at the building.