Swedish author Jan Lööf. Photo: Erik Abel/TT
The two books – called "Morfar är sjörövare" and "Ta fast Fabian" – were reviewed by publishers Bonnier Carlsen.
"They've given me an ultimatum. I either have to redraw the pictures or the books won't be published anymore," the author told the Dagens Nyheter newspaper
One of the books, "Morfar är sjörövare" (which translates as "Grandfather is a Pirate"), was published back in 1966 and has since been translated into several languages.
In it, the main character meets a street seller named Abdullah and an evil pirate called Omar, who is pictured in the tweet below.
The books have proved hugely popular in Sweden, with copies given out free by McDonald's in the past.
The other book, which was published in 1997, has pictures of what appears to be a bongo drummer dressed in bangles, paint, a skirt, a headdress, and sunglasses. The rest of the band wear formal attire.
Eva Dahlin, a spokesperson from Bonnier Carlsen, said that it was "unfortunate" that Lööf interpreted the decision as "an ultimatum".
"This is about stereotypical depictions of other cultures, something that's not so strange considering all the pictures were created in a context, in their time, which changes. If you've got a Middle Eastern background, for example, you can get tired of rarely being portrayed as being one of the good guys in literature," she said.
She added that it was important to see it from the perspective of a child who simply doesn't have the historical context to understand the pictures.
Author Jan Lööf, meanwhile, can't see himself changing the books.
"I'm 76 years old and can't be bothered to change. This isn't about the money. But, I probably won't be doing any more books for children," he said.
There has been general support for Lööf on Sweden's social media channels, with many social media users questioning whether censorship has gone too far.
The user below, for example, has said that "Grandfather is a Pirate" will "obviously be bedtime reading tonight".
Sweden has had struggles with culturally insensitive depictions in art in the past.
In 2012, advertisement posters for a children’s film were pulled down
over concerns that one of the pictured characters has stereotypical "racist" undertones after one character was depicted with a black face, braided hair, white eyes and oversized, full white lips.
In the same year, there were calls for the former minister of culture to resign after she carved up a cake depicting a naked black woman, in an act that was described as "a racist spectacle