Cancerfonden's video featured animated women with their breasts represented by pink circles, showing ways to detect suspicious lumps.
The images were considered "offensive" by the social media platform.
The social media website caused outrage last month for removing the "napalm girl" photo, saying it showed nudity.
It later reversed that decision, allowing the publication of the iconic picture which shows a badly burned fleeing a napalm attack during the Vietnam War.
In a statement to the BBC, a spokeswoman for Facebook said the images of the Swedish campaign had now been approved.
"We're very sorry, our team processes millions of advertising images each week, and in some instances we incorrectly prohibit ads," she said.
"This image does not violate our ad policies. We apologise for the error and have let the advertiser know we are approving their ads."
Before the decision was reversed, Cancerfonden had said in an open letter to Facebook that the campaign "was not meant to offend".
It added that it had found a solution to the problem: illustrating breasts using two pink squares.