The competition was started by Kostbar in March, The Copenhagen Port reported Monday.
To win a pair of fake breasts, contestants were asked to send in a photo along with a brief explanation of why they should win. The photos and descriptions were then posted to the bar's Facebook page and the winner would be the individual whose photo had the most number of "likes."
In the last week of the competition, trans woman Malene Lang Hansen was in first place with about 1,600 votes.
"I am transsexual and was born in a boy's body," she wrote in her photo description. "On the inside I have always felt like a woman."
But, just days before the contest was over on June 1, a new competitor emerged who quickly gained almost 4,000 votes, bumping Hansen to second place and leading others to believe the contest was rigged against her.
"I think it's very suspicious that two days before the end of the competition a new girl suddenly shows up who quickly gains 3,700 votes," Hansen told the Politiken newspaper. "I, and many others, think the Kostbar has cheated. I am the moral winner of the silicone breasts but obviously it didn't fit their advertising campaign."
Hansen added that the incident brings to light the discrimination faced by transgender people.
"It's really hard work to get acknowledgement and respect when you are transsexual. This case shows the discrimination transsexual people face. It shows the distance and the contempt that transsexuals and other minorities experience."
Kostbar owner Thomas Sogaard has denied the contest was rigged to prevent Hansen from winning the breasts.
"We have had no influence on the result of the competition," Sogaard wrote on Facebook. "We are sorry that a participant is sad not to have won but the same rules applied to everyone. We cannot give a prize for second place as that would be unfair to the other participants. We wish the winner congratulations and thank everyone for the interest that has been shown for the competition."