In order to prevent the further spread of COVID-19 in the country, Kazakhstan has decided to reintroduce the visa for entering the country. Visitors will have to show a medical certificate, not older than two days, proving they don’t have the virus. More information on this temporarily change of policy can be found here.
Kyrgyzstan and Uzbekistan, the other two visa free countries in Central Asia, have not (yet) decided to request a visa. They do need the revenues from tourism more than much richer Kazakhstan.