In Europe, Albania doesn't have a zoo (there was Tirana zoo but possibly now is non-existent or is limited to a city park with some animals like fox, pigeons). Montenegro seems that does not have a zoo, also the state of Kosovo (2 millions people) (which declared independence in 2008 from Serbia) doesn't have a zoo.
Bhutan doesn't really have a zoo, but it does have the Motithang Takin Preserve (I guess that does not count). I think many African countries lack zoos. Along with Botswana and Equatorial Guinea, Namibia, Mauritania, Cape Verde, Lesotho, Swaziland, Zimbabwe, Somalia, Guinea, Djibouti, Togo + some more....(according to Wikipedia) do not have zoos.