The video, verified by the Reuters news agency, shows the plane heading towards the ground at high speed with the landing gear down.
Seconds after it appears to be trying to land, a huge fireball erupts.
There were 62 passengers and 5 crew members on board the Embraer 190 plane, the Ministry of Transport reported.
On board were mainly citizens of Azerbaijan, but there were also passengers from Russia, Kazakhstan and Kyrgyzstan.
Aktau Airport is open and operating normally, the authorities said.
The BBC has contacted Azerbaijan Airlines and Embraer for comment.
