The young girl was believed to have begun her journey in Nigeria, which is one of the countries affected by the Ebola outbreak.
Public health specialists boarded the plane on Sunday. The other passengers left more than two hours later.
It was later confirmed it was not a case of Ebola.
John Wood, the father of a pregnant woman who was passenger on the plane, told the BBC Scotland news website: "She said it was a nightmare trip - they were in biohazard suits which was alarming.
"They sealed the plane and the passengers were stuck on as they decided the next step.
"They need to put minds at rest, there is conflicting information and we want a definitive answer that no-one is at risk."
A spokesman for the Scottish Ambulance Service said that when specialist operations paramedics arrived the aircraft had already been quarantined.
Paramedics boarding the aircraft wearing protective biohazard suits was described as a "standard precaution".
The spokesman said that after liaising with the pilot and an assessment of the patient it was decided her illness was low risk.
The patient was taken to hospital by ambulance.
Special health control measures were put in place at Aberdeen International Airport after a passenger complained of feeling ill.