A teenage boy died after a window frame fell on him, the health ministry said in a statement, adding that 24 people had been hospitalised, but faced no threat to their lives, while 138 were treated for injuries.
Flights were operating as normal at the international airport in the capital, its administration said.
In video and photographs on social media, flames soared into the night sky, with a huge cloud of smoke hanging above the warehouse, but the cause of the explosion was not immediately clear.
A special laboratory had been set up at the scene to investigate the blast, the emergencies ministry said.
"As a result of the quick actions of emergencies ministry employees, the area of the fire is being reduced," it added on the Telegram messaging app.
"The situation is completely under control."
A social media post from Uzbek outlet Daryo said 16 fire and rescue crews were sent to fight the fire at one of the warehouses in the city's Sergeli district near the airport.