The fine is for 20,000 Norwegian crowns ($2,352), police chief Ole Saeverud told a news conference.
The matter came to light in a report by Norway’s public broadcaster NRK, which triggered the police investigation.
The two-term Premier has apologised several times for organising the event for her 60th birthday with 13 relatives-at a mountain resort, despite a government ban on gatherings of more than 10 people.
Meanwhile she later accepted the fine and said she would pay.
“I’d like to say again that I’m sorry for breaking the coronavirus rules,” she said.
“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 has been at the forefront of the government’s work to impose 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.
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.