Most of the external parasites of domestic dogs and cats (fleas, mange mites, ear mites, etc) can cause disease in ferrets. Less is known about the ferret's susceptibility to the more common internal parasites (roundworms, etc) of dogs and cats. Protozoan (one-celled) parasites, also shared by dogs and cats (especially Giardia and coccidia), can cause intestinal disease among ferrets. Periodic fecal (stool) examinations should be performed by your veterinarian to heck for such parasites. Appropriate treatment can then be given, if warranted.
Ringworm (a fungal disease of the skin similar to Athlete's foot): Has been reported in young ferrets and may be transmitted by infected cats. As a rule of thumb, products manufactured and intended for use in and on cats (dewormers, flea products, ringworm medications, etc) are safe and suitable for use in and on ferrets, with one exception: flea collars should never be used on ferrets.
Heartworm Disease: Ferrets are susceptible to heartworm disease, a mosquito-transmitted illness seen primarily in dogs. Ferret owners must carefully consider the pros and cons of preventive therapy for this disease. Some ferrets may have adverse reactions to the drug used for heartworm prevention. Furthermore, the average pet ferret is very unlikely to be bitten by an infected mosquito unless it lives in an area of heavy heartworm infection and is often exposed (housed outdoors) to mosquitoes. Most pet ferrets housed exclusively indoors are unlikely to become infected by heartworms and should not require preventive therapy.