The picture is headlined "June 25 | Pride," and an accompanying text reads "Proudly support love!"
Basil Maglaris, Kraft's associate director of corporate affairs, said the graphic was in recognition of Pride Month in the United States.
More than 150,000 Facebook users "liked" the post and 22,463 had commented as of Tuesday afternoon. Not all the comments were supportive.
One comment read: "By (sic) Oreo. I'll do my business elsewhere!"
Another said: "No thanks Oreo. We don't want this unhealthy sinful lifestyle flaunted," and a third read: "thought Oreos were a family cookie."
Maglaris said positive comments have "far outnumbered" negative ones.
One read: "Very glad to support a company like Oreo that joins the campaign for civil rights!"
"As a company, Kraft Foods has a proud history of celebrating diversity and inclusiveness. We feel the Oreo ad is a fun reflection of our values," Maglaris said.
The ad was part of Oreo's 100th birthday celebration, he said. The company posts new online content daily.
Don't look for the rainbow cookie in stores. Fine print under the picture reads: "Made with creme colors that do not exist."