The cartoon, by Norwegian cartoonist Ola Lysgaard, shows a woman standing in front of an organic food store.
"Organic food, huh?" reads the text. "But who cares if the food is produced unethically?"
In the next panel, the woman holds an orange and says: "These oranges comes from Israel! You are supporting murderers!".
Next the woman is seen holding a carton: "This macaroni is produced in North Korea!? How did you even get a hold of these??".
In the last panel, the woman holds a box of frozen pizza marked with a swastika, with a "Made in Nazi Germany" label, and says: "And this pizza is from N… what kind of store is this??"
Dan Poraz, first secretary at the Israeli Embassy in Oslo, said that the cartoon was "thoughtless" and "reprehensible" and clearly constituted hate speech.
"There is a fine line between freedom of speech and hate speech," he wrote in a comment in Dagbladet, "and this cartoon crossed that line, it's about time that editors take responsibility. An apology may be a suitable way to start."
He complained that the cartoon "puts Israel in the same category as Nazi Germany and North Korea", and compared "democratic Israel, which fights for the security of its citizens" with "unstable and violent dictatorships".
He also said it was both "incorrect" and "offensive" to portray Israeli products as "unethical".
"This is damaging because it can incite anti-Israeli bias that can lead to violent reactions," he said.
According to Israel's Ynet News, Dagbladet's editor has refused to apologize, arguing that it was "only a cartoon" and that the Israeli reaction was overblown.
The cartoonist Ola Lysgaard is bemused by the stir.
"I'm used to people not getting my jokes. They aren't trying to please everyone. But I've never experienced people missing the point to this extreme level," he told the Local.
"I don't know if the offended people read a bad translation, or just didn't get it. Either way, I can't help but find the whole situation utterly amusing."