Internal parasites
Adult ferrets are rarely affected by internal parasites such as worms, but juvenile ferrets (whose immune systems are not fully developed) are susceptible to coccidiosis and Giardia – protozoal (single-celled) parasites that cause severe diarrhoea and weight loss. Your ferret should be assessed for these parasites on their first physical exam by a veterinarian and treated as appropriate. There are no suitable pet shop or over-the-counter remedies available. Ferrets living indoors with no access to other ferrets outside their group are unlikely to require treatment for internal parasites after this initial screening. However, ferrets who are kept close to dogs or handled regularly may be at risk of canine roundworm, so speak to your veterinarian for advice about monitoring and treatment.
External parasites
External parasites are a different matter. Ferrets are commonly infected with flea burdens and ear mites, both of which can be contracted from other ferrets as well as dogs and cats. Many ferrets carry ear mites and can infect other ferrets if they are not screened before being added to your group. Fortunately, treatment and prevention are easy these days, with a variety of effective topically applied medications available. Your veterinarian can advise you which products are the most effective and safest for your ferrets.
Heartworm
Ferrets can be infected with heartworm, the same parasite that can infect dogs (and sometimes cats). It is spread by mosquitos, so direct contact with a dog (or cat) is not necessary. Although heartworm can be treated, the treatment can be both expensive and potentially dangerous. Prevention is the best approach, usually medication given by mouth or applied to the skin once monthly (some of these medications will treat for fleas and ear mites as well). Again, your veterinarian is the best person to talk to about prevention.
References
Vinke C, Schoemaker N, van Zeeland Y (2019) Ferrets (Mustela putorius furo). The UFAW Companion Animal Handbook
Harris L (2015) Ferret Wellness Management and Environmental Enrichment. Veterinary Clinics of North America: Exotic Animal Practice 18:233–244
Chitty JR, Johnson-Delaney CA (2016) Ferret Preventive Care. In: Ferret Medicine and Surgery, 1st ed. CRC Press, pp 85–93