"It sleeps, don't make noise at night," according to the Craigslist advertisement placed last Friday.
And the seller offered to throw in clothes, formula - and even the infant's four-year-old sister - for free.
All for the price of $US500.
Now on the Florida Department of Law Enforcement has launched an investigation.
"I don't wanna be judged for not wanting these kids," the ad's poster wrote, adding they lived in a quiet influential neighbourhood and worked for the Department of Children and Families.
Investigators told the Miami Herald they remained unsure whether the ad was nothing more than a crude hoax, and were waiting on computer records that might help identify the poster.
"We do have an active investigation that started last Friday," FDLE spokeswoman, Gretl Plessinger, said.
Neither Craigslist or the Florida Department of Children and Families responded to the newspaper's request for comment.
This story first appeared on 7NEWS and has been republished here with permission.
