Video verified by Reuters news agency shows the plane heading towards the ground at high speed, with its landing gear down.
Seconds after it seems to attempt to land, a huge fireball erupts.
The airline said the plane “made an emergency landing” about 3km (1.9 miles) from Aktau.
It took off from Baku at 03:55 GMT on Wednesday, and crashed around 06:28, data from flight-tracking website Flightradar24 showed.
There were 62 passengers and 5 crew members on board the Embraer 190 aircraft, the transport ministry said.
Those on board were mostly Azerbaijani nationals, but there were also some passengers from Russia, Kazakhstan, and Kyrgyzstan.
Out of the 25 known survivors, 22 were taken to hospital, the emergency ministry said.
Unverified video footage showed emergency services putting out a fire and pulling people out of the wreckage.
The government has launched an investigation into the cause of the accident. Embraer told the BBC it was “ready to assist all relevant authorities”.
The BBC has contacted Azerbaijan Airlines for comment.
