The remake of the classic is the first Disney feature film to have an openly gay character. It features Lefou (featured in the top video, below) having feelings for Gaston.
The evangelist and president of aid charity Samaritan's Purse, who is son of the renowned evangelist Billy Graham, lamented that Walt Disney would be shocked at the decision the company he founded has made.
Graham's call for a boycott has got more than 47,000 likes on Facebook, however around double expressed dislike or anger at it.
His comments come as other Christian leaders across America urge believers to boycott the film as well.
He said on Facebook: "They're trying to push the LGBT agenda into the hearts and minds of your children - watch out!
"Disney has the right to make their cartoons, it's a free country. But as Christians we also have the right not to support their company. I hope Christians everywhere will say no to Disney.
"I met Walt Disney when I was a young boy - he was very gracious to me, my father Billy Graham, and my younger brother when we visited. He would be shocked at what has happened to the company that he started."
Director of the new Beauty and the Beast film Bill Condon told Attitude Magazine: "It's somebody who's just realising that he has these feelings. And Josh [the actor] makes something really subtle and delicious out of it.
"It is a nice, exclusively gay moment in a Disney movie."