Unverified videos on social media purported to show large columns of black smoke over the city's skyline, while another showed drones buzzing overhead.
Further footage shows bystanders screaming in terror as explosions rang out and what appears to be a rocket flies overhead, while smoke pours from an apartment block.
The large-scale attack came hours before Russian President Vladimir Putin was set to meet Southeast Asian leaders at a summit in the central city of Kazan, about 700 kilometres (435 miles) east of the capital.