“At 7:00 pm (1600 GMT) Moscow time, there were three dead and three injured,” emergencies ministry representative Pyotr Fomin said in televised remarks.
“One child is among the dead,” added Alexander Brechalov, the head of the Udmurtia region of which Izhevsk is the capital.
According to the local health ministry, a member of the rescue team was also injured.
The cause of the collapse was likely a gas explosion and other residents have been evacuated from the building, emergencies ministry official Igor Kutrovsky said.
A representative of the Investigative Committee, Vera Filippova, said a probe into the collapse has been launched.
According to the emergencies ministry, the building collapsed in the late afternoon, and video footage showed flats on all nine floors reduced to debris, with dust rising from the pile.
A total of eight apartments were completely destroyed and 220 rescuers were on the scene looking for survivors.
The damaged building is a typical Soviet-era residential block made of concrete panels.
“There was the sound of such a loud blast that even the building shook,” a witness named Olga who lives in a neighbouring building told state television.
Fomin told TASS news agency that the collapsed area had 28 residents, estimating that “not more than 10-15 people” were at home when the accident happened.
The ministry sent reinforcements to Izhevsk, which is located some 940 kilometres (585 miles) east of Moscow, and has a population of about 650,000.
Explosions caused by natural gas leaks are frequent in Russia, especially in older Soviet-era buildings.
The last serious gas explosion in February 2016 killed seven people, including two children, when part of a block of flats collapsed in the city of Yaroslavl, north of Moscow.
Another in February 2012 killed 10 people in the southern city of Astrakhan and destroyed the entire side of a nine-storey building.