Officials in Izhevsk believe a natural gas explosion is the most likely cause. Such blasts are common in Russia, where bottled gas is often used for cooking at home.
Pyotr Fomin, head of the local branch of the Emergencies Ministry, said in televised remarks that search teams have rescued three people, who were hospitalised with injuries, and pulled out three bodies from beneath the rubble.
Officials said more people are believed to remain under the debris.
Izhevsk, a city of about 625,000 people is about 1,200 km east of Moscow, is home to many industrial plants, including a factory that makes Kalashnikov assault rifles and other weapons.