The next 'approved' Traditional Latin Mass will be on May 31 (Pentecost), but usually it is offered every 1st Sunday of the month, at 1700 H (5:00 P.M.) in the basement chapel of the Cathedral (of the Immaculate Conception, Moscow).
The priest who offers the Mass is Fr. Augustyn Dziedziel SDB (pronounced Dzendzel and written in Polish with a special mark under the first e, ę in HTML). Catholic guests of Moscow are most welcome. (Father also speaks some English in addition to Polish and Russian, so confessions are possible before Mass.)
Traditional Latin Mass in Moscow, Russia
From Una Voce Russia, and edited for posting on Rorate: