"Six people including a 14-year-old girl were crushed by trees, and a man was crushed when his lorry overturned," the local branch of the ministry of emergency situations said.
Fourteen people were injured, four of whom are in a serious condition, the ministry said.
An unprecedented heatwave across western Russia have caused forest fires that have destroyed homes.
Prime minister Vladimir Putin visited one of the worst hit areas on Friday to reassure distraught residents.
People in a village in the central Nizhny Novgorod region where all 341 houses burnt down confronted Putin as he toured the area, many wiping tears from their eyes, television reports showed.
Putin promised residents that all the houses will be rebuilt by the winter
More than 2,000 people have been left homeless and nearly 132,000 people have lost electricity due to the storm.