The blaze tore through a private children's tent camp near the city of Komsomolsk-on-Amur in the Khabarovsk region, destroying 20 tents and killing a girl on her 11th birthday.
Two other girls and a boy suffered extensive burns and later died in hospital, officials said.
"Four children have become victims of the fire," the Investigative Committee said in a statement.
A spokeswoman for the regional authorities, Nadezhda Tomchenko, said the children's "injuries were incompatible with life".
The camp was being attended by 189 children and teenagers aged between seven and 15.
Prime Minister Dmitry Medvedev publicly berated the regional governor for apparently saying that officials did not know about the existence of the private camp.
"What kind of statement is that? If no one knew, that means that they didn't carry out their duties properly. And if they knew, why did they allow it?" Medvedev said.
Investigators launched a manslaughter probe, and two people including the director of the tent camp were detained.
Fires are common in Russia and often kill the most vulnerable due to negligence and disregard for safety rules.