The posting asks followers to "like" the image if they think toy companies should make the fuller-figure dolls and to comment if not.
As of midday Saturday, more than 40,000 people had "liked" the image, and more than 5,000 had left comments disagreeing with the idea.
Several commenters were outraged over what they said was promoting a morbidly obese lifestyle.
"No one is naturally fat for gods sake, that's sending the message to girls that it's ok to look like this and be unhealthy.. How about we stop obsessing about being overweight and teach our children to eat healthy and get out and play," one person said.
"Why not have a realistically proportioned Barbie that promotes healthy diet and exercise?" one commenter asked.
"Sure, but Barbie doesn't need a double chin. You can be 'plus size' w/o the double chin. They could make a 'thick' Barbie," one commenter said.