In the United States, 10 zoos keep koalas: San Diego, Los Angeles, San Francisco, Columbus, Cleveland, Miami, Riverbanks, Palm Beach, Lowry Park, and Toledo.
According to zootierliste Germany Dresden (Zoo) Duisburg (Zoo) Leipzig (Zoo) Austria: Wien (Tiergarten Schönbrunn) Belgium: Antwerpen (Zoo) Cambron-Casteau (Pairi Daiza - vormals Parc Paradisio) Mechelen (Dierenpark Planckendael) France: Saint Aignan (ZooParc de Beauval) Portugal: Lisboa (Zoo) Spain: Madrid (Zoo/Aquarium) UK/Scotland: Edinburgh (Zoo) Israel: Victoria koala Nir David (Gan Garoo Australia Park)
Australia: Darling Downs Zoo, Australia Zoo, David Fleay Wildlife Park, Currumbin Sanctuary and probably many others...
It seems every other zoo in Australia has koalas. In zooboy28's Native Mammals in Australian Zoos thread he lists it as "very common" = 20+ Australian zoos with the species. At least until very recently there were also koalas in zoos in Japan, Thailand and Singapore, but I'm not sure how many of them remain today.
There are still ~ 40 koalas in Japan, but that’s down from 60 a decade or two ago. Part of this decline is due to koala retrovirus (KoRV) which most Japanese koalas have.
As a rough estimate I made once, there are probably about 1000 Koala in captivity in Australian collections.