From Una Voce Russia, and edited for posting on Rorate:
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.)