The online giant stopped short of apologizing, saying the image had been flagged for violating standards regarding inappropriate posts at the world's leading social network.
"An image of a naked child would normally be presumed to violate our Community Standards, and in some countries might even qualify as child pornography," Facebook said in a statement.
"In this case, we recognize the history and global importance of this image in documenting a particular moment in time."
Taken by photographer Nick Ut Cong Huynh for the Associated Press, the 1972 picture of a naked Vietnamese girl running from a napalm attack is considered one of the war's defining images. It was honoured with the Pulitzer Prize.
Earlier on Friday, Norwegian PM Erna Solberg posted the photo in response to an ongoing controversy that had been brewing in the Nordic nation since Facebook deleted a post from author and journalist Tom Egeland that contained the pic and then subsequently banned him from the site.
Several Norwegian media outlets and private Facebook users came to Egeland's defence and posted the photo in direct challenge to the social media giant's censorship. Each time, it was deleted.
Solberg's post was also removed from the site within hours in what is believed to be Facebook's first such censorship involving a government leader.
Screenshot of the PM's Facebook post
The PM wrote that she values Facebook's efforts to “stop photos and content that show abuse and violence” but said the social media giant was clearly wrong in this case.
“Facebook is making a mistake when it censors these types of photos. It contributes to limiting the freedom of expression,” Solberg wrote. "I support a healthy, open and free debate – online and elsewhere. But I say no to this type of censorship."
After her first post was deleted, the PM reposted the 'napalm girl' photo along with other iconic historical images with large black boxes obscuring their content.
"While I was on a plane from Oslo to Trondheim, Facebook deleted a post from my Facebook page," she wrote. "What Facebook does by removing images of this kind, good as the intentions may be, is to edit our common history."
She called on the social media giant to "review its editing policy".
"I want my children and other children to grow up in a society where history is taught as it was. Where they can learn from historical events and mistakes," Solberg wrote. "Today, pictures are such an important element in making an impression, that if you edit past events or people, you change history and you change reality."
Also on Friday, Norway's largest newspaper Aftenposten published an open letter to Facebook founder Mark Zuckerberg that accused him of "punish[ing]" users who dare to criticize "the world's most powerful editor".
Aftenposten splashed the photo on its front page and ran an open letter to Zuckerberg from editor-in-chief Espen Egil Hansen blasting Facebook for “abusing [its] power” and threatening editorial freedom.
The newspaper also posted a video message to Facebook refusing to remove the photo:
“Even though I am editor-in-chief of Norway's largest newspaper, I have to realize that you are restricting my room for exercising my editorial responsibility. This is what you and your subordinates are doing in this case,” Hansen wrote.
“I think you are abusing your power, and I find it hard to believe that you have thought it through thoroughly,” he continued.
Hansen then accused Facebook of stifling criticism by deleting Egeland's post calling out the network's censorship.
“Listen, Mark, this is serious. First you create rules that don't distinguish between child pornography and famous war photographs. Then you practice these rules without allowing space for good judgement. Finally you even censor criticism against and a discussion about the decision – and you punish the person who dares to voice criticism,” he wrote.
“If you will not distinguish between child pornography and documentary photographs from a war, this will simply promote stupidity and fail to bring human beings closer to each other. To pretend that it is possible to create common, global rules for what may and what may not be published, only throws dust into peoples' eyes,” Hansen continued.
The full letter can be read here (in English).
AFP contributed to this story.