The matter came to light in a report by the public broadcaster NRK, which triggered a police investigation.
The two-term leader has apologised several times for organising the event for her 60th birthday with 13 relatives at a mountain resort in late February, despite a government ban on gatherings of more than 10 people.
Solberg said on Friday she would pay the fine, which was issued by police.
"I'd like to say again that I'm sorry for breaking the coronavirus rules," she told Norway's TV2 News. "I will accept the fine, and pay it."
While police would not have issued a fine in most such cases, they said the prime minister had been at the forefront of the government's work to impose restrictions.
"Though the law is the same for all, all are not equal in front of the law," the police chief, Ole Saeverud, told a news conference, justifying the fine. "It is therefore correct to issue a fine in order to uphold the general public's trust in the rules on social restrictions."
Police said Solberg and her husband, Sindre Finnes, made the decision together to hold a celebration and picked the restaurant, with Finnes taking care of the practical arrangements.
Comment: Clearly she chose to stay despite knowing it contravened her own diktats.
Though police said he had broken the law as well, he was not fined. The restaurant where the celebration took place was also found to have violated the law but not penalised.
"Solberg is the country's leader and she has been at the forefront of the restrictions imposed to limit the spread of the virus," said Saeverud.
Solberg, who faces elections for parliament in September, has championed strict rules to curb the spread of the coronavirus, resulting in some of Europe's lowest rates of infection and deaths.
But Norway saw a rapid rise in infections in the first quarter of 2021, led by more contagious variants of the virus, forcing the government to tighten restrictions in late March.
Comment: Politicians throughout the West have been telling citizens to hold 'virtual' events of all kinds - from Christmas to funerals - why did the PM decide this did not apply to her? If the PM genuinely thought the coronavirus posed such a risk to life - that she's willing to enforce livelihood destroying lockdowns - why did she stay to celebrate at her in-person birthday party?
Meanwhile in the real world: French clergymen ARRESTED over lockdown-breaking Easter mass attended by hundreds of worshipers