Preliminary reports suggest there are 25 survivors, 22 of whom have been taken to hospital, Kazakhstan's emergency ministry said.
The plane, operated by Azerbaijan Airlines, caught fire as it went down near the city of Aktau but the fire has since been put out, officials said.
Azerbaijan Airlines flight J2-8243 was en-route from Azerbaijani capital Baku to Grozny in Russia. Reports say it was diverted because of fog.