Since Monday night, nearly 200,000 people have liked the post, 60,000 have shared it, and 30,000 have commented on it.
Most of the comments were positive, but some people threatened to boycott Oreo because of the post.
The rainbow-colored cookie will not be sold in stores.
It was just created for an advertising campaign during Gay Pride month.
Kraft said it has a proud history of celebrating diversity and inclusiveness.
2012 WGCL-TV (Meredith Corporation).