The attacker, who was arrested on the spot, broke into the Hasid Synagogue on Bolshaya Bronnaya Street during a prayer service.
Police have identified him as Aleksandr Koptsev, a 20-year-old unemployed Moscow resident. His motives remain unclear.
Investigators say they have no reason to believe Koptsev is linked with any extremist organization. They say he recently suffered a family trauma that could have affected his behavior.
The Ekho Moskvy radio station quoted Rabbi Itzakh Kogan, who himself was wounded in the assault, as saying four people sustained serious injuries. Moscow Prosecutor Anatoly Zuyev said one American, one Tajik, and one Israeli national were among the wounded.
The Israeli Embassy in Moscow said it was "extremely concerned" by the incident. The Russian Orthodox Church condemned the attack.
(ITAR-TASS/Ekho Moskvy/RIA Novosti/Interfax)