Although caring for pets can be beneficial for children, many animals such as tortoises carry diseases such as rabies or salmonella which can be transferred to their young owners, the study in the October edition of the Journal of the American Academy of Pediatrics said.
Other more exotic creatures such as iguanas and monkeys can bite or scratch children causing infected wounds or allergies.
The study highlighted that most American homes have one or more pets, and recommended that families with children under the age of five should avoid adopting exotic animals.
The report said 11 percent of salmonella cases in children resulted from contacts with lizards, turtles and other reptiles, said lead author Larry Pickering.
Some 40,000 US homes have hedgehogs as pets, which are also carriers of two other kinds of salmonella found in their spines.
"Exotic animals imported to the United States have been associated with the introduction of infectious agents otherwise not present in the United States," the study says.
"Contact between animals from different areas of the world can lead to the appearance of disease in a new species and establishment of a pathogen in a new geographic area."
One example given is the arrival of human monkeypox in the United States in 2003, which was traced to an importation of African Gambian rats, which infected prairie dogs sold as pets.
The report also warned that "the natural reservoir of plague is wild rodents with humans becoming infected through bites of infected rodent fleas."
It highlighted that macaque monkeys have been found to carry a type of Herpes B virus, while cases of a nasty lymph disease known as tularemia, which can lead to painful skin and mouth ulcers as well as pneumonia, have been traced to hamsters.
"Most non-traditional pets pose a risk to the health of young children, and their acquisition and ownership should be discouraged in households with young children," the report concludes.