The poster shows what looks like one of the company's famous building blocks.
It reads "Racism takes many shapes" and shows a picture of a jigsaw puzzle next to a red brick. It was launched by the UN to mark the International Day for the Elimination of Racial Discrimination.
"We feel that the message of this poster can be interpreted as if we are a racist company," Lego spokeswoman Charlotte Simonsen said.
"I don't know if that's what's intended, but it's definitely one way of interpreting it."
However, the UN said no affiliation to Lego was intended and apologised for the misunderstanding.
"The poster is in no way a comment on the specific situation in Denmark or on Lego," a spokesperson said.
"It is unfortunate that the poster has been interpreted as such."