Another user tweeted to the Centre for Disease Control - the US health agency overseeing the operation to contain the virus - "Who is unprotected clipboard dude...so we can all stay the hell away from him!"
It later emerged he works for the air ambulance company that handled the flight.
Amber Vinson became the second nurse from Dallas Presbyterian Hospital to be diagnosed with Ebola after caring for Thomas Eric Duncan, who died there last week. About 75 other members of the medical team are being monitored for signs of the disease.
Miss Vinson was being airlifted to Emory University Hospital in Atlanta, where Ebola experts have successfully treated other patients who contracted the disease in Africa, when the photographs of the "clipboard man" were taken.
Miss Vinson told authorities that she had flown from Cleveland back to the Texas City on Monday, the day before she became ill, through airports used by tens of thousands of passengers each day.
President Barack Obama was forced to cancel a campaign trip to hold an emergency Ebola summit at the White House amid growing condemnation of the chaotic federal response to the arrival of the disease in the United States.
App users: Watch the 'clipboard man' video here
In wake of the criticism, he pledged that US monitoring of would be Ebola "much more aggressive" and that the Centre for Disease Control would send a "SWAT team" within 24 hours to any hospital encountering a new case.
He warned that the disease could spread globally if the international community does not do more to tackle the outbreak in Africa as he urged world leaders to step up their efforts to defeat it there.