Boris Dzgoyev, the emergency situations minister in the North Ossetia province, said on Friday that the explosions occurred around the same time on Thursday night at gambling establishments in Vladikavkaz.
Police said that according to a preliminary investigation, each bomb was a remote-controlled device equivalent in force to 300-400 grammes of TNT and filled with screws to inflict maximum casualties.
The ministry said that one of the dead was a 26-year-old woman and the other was a 34-year-old man. Five of the 22 wounded are in serious condition.
Schools were shut on Friday in the city as security was tightened. There was no claim of responsibility.
Prosecutors were treating the blasts as terrorism, Alexander Panov, the deputy regional prosecutor, said. He said that investigators had not excluded the possibility that the attack was tied to the gambling industry.
On Wednesday, a new law toughening regulations on the gambling industry went into effect in North Ossetia.
It significantly increased the tax burden, restricted hours of operation and limited the places where gambling would be allowed to outside city limits.