There were more than 300 soldiers in the training facility for paratroopers when the accident happened overnight. The building underwent repairs a year ago. It is suspected that poor quality work may have caused the collapse.
An investigation into possible negligence has been launched.
All 19 soldiers pulled out of the rubble alive were injured, and the most seriously hurt were taken to Moscow for treatment. One survivor, shown on Russian television, said troops just gone to bed when the four-storey building began collapsing on top of them.
President Vladimir Putin has expressed his condolences.