The Almaty municipality said in a statement that dozens of people were evacuated from a neighbouring apartment block as the flames and black smoke spread high into the sky.
"The petrol tanker overturned and exploded, leaking petrol. Eight vehicles caught fire. The flames reached the ninth floor of the residential block," it said in a statement.
"The driver was killed on the spot, there are no other victims."
Almaty, in the extreme south east close to the border with China, was capital of Kazakhstan until 1998 when the capital was moved to Astana which is more in the centre of the country.
