NAIROBI—The outbreak of the Ebola virus in West Africa is hitting many African economies where they are most vulnerable—the tourism industry—as travelers reconsider trips to places as far away as Kenya and South Africa.

Fear of the virus is rattling would-be tourists to the continent and is underlining the risks some associate with travel to Africa. Anxious African governments have potentially amplified those worries with their own draconian measures to keep the virus from breaching borders.

Government tourist boards and trade associations have issued statements trying to assuage fears, but operators say they are still getting anxious phone calls, fewer bookings and abrupt cancellations.

One Thai insurance company that had booked a trip to Cape Town to reward its biggest earners canceled the trip for 1,500 people, said Barry Hurter, the chief executive of South Africa's ERM Tours, which runs excursions that include safaris and corporate retreats.

(Ebola virus: Liberia's president orders curfew and quarantine).