Four of those who were wounded are in a serious condition, reports say.
Rabbi Yitzhak Kogan, quoted by Itar-Tass, said the attacker had shouted "I will kill you" before lashing out indiscriminately with his knife.
Besides being described as a skinhead the man has been identified as a 20-year-old Muscovite.
Russia's Chief Rabbi Berl Lazar said he was cutting short a visit to Israel and going back to Moscow and he called on the Russian authorities to fight the "brown plague" of fascism.
There have been a number of attacks on synagogues and Jewish centres across Russia in recent years.