The attack took place on Tuesday and affected eight companies - Norges Bank, Telenor, DNB, Sparebank 1, Nordea, Danske Bank, plus insurance companies Storebrand and Gjensidige.
The companies' websites and online payment systems were hit and all encountered serious IT problems from Tuesday morning until later in the evening the same day.
It is the first hacking attack of its kind to hit so many major firms, said IT experts Evry.
Sverre Olesen, manager of Evry's security team, said in Dagens Næringsliv: "The extent of the attack is not the greatest we have seen, but it is the first time that such an attack has hit so many central agencies in the financial sector in Norway. Several sectors are affected, but I cannot be certain whether these are random targets or not."
The attack is thought to have come from hackers based outside Norway. They tried to exploit a weakness in the mainstream computer software Wordpress. The hackers sought to control web traffic to the websites of the financial institutions and many websites crashed, causing customers problems accessing the sites.
Internet activist group “Anonymous Norway” claims to be behind the attack, said Dagens Næringsliv.