Moderna Museet in Stockholm took a head start and implemented this new policy two weeks ago and, even if it is a little early to assess the results, its co-director Ann-Sofi Noring already sees some changes.
"People are a little bit more easy-going, and I would guess that there are people who would not come back as often as they will now because now you don't have this obstacle, the economic obstacle," she tells Radio Sweden.
Yasmine Farhadian, a 27-year-old nurse, visited Moderna Museet for the first time on Tuesday. She says that the absence of an entrance fee was an important factor.
"It's very good that it's free and you can come on a free day and just walk around," Farhadian says.
The government wants to see more men, foreign-born citizens and people with lower levels of education in Swedish museums. But this initiative is not new, museums were also free in 2005 and 2006.
Sverker Härd, head of the Swedish Agency for Cultural Policy Analysis, analyzed the results of that period.
"That reform, and most likely this one about free entrance, will increase the number of visitors. But we can't be equally sure that new groups will go to museums. We could also be talking about frequent visitors who decide to go more often," he tells Swedish Radio News.
Noring agrees that the financial factor is only one among many others in this challenging task.
"Economy is not the only obstacle for people to attend museums. It deals with your background, with schools, with the upbringing," Noring says.
Some of the complementary measures planned by Moderna Museet include increasing the number of free guided tours, which will be offered in a broader selection of languages.