Moskvin was born on 30 August 1929[1] in Bezhitsa, Bryansk Oblast.[2] He married Tamara Moskvina (née Bratus) in 1964.[2][3] They have two daughters, Olga Igorevna Moskvina (born 12 April 1970),[1] and Anna Igorevna Moskvina (born 14 June 1974).[2][4] He and his wife reside in Saint Petersburg.
Moskvin died in November 2020 after a serious illness.[5]
After ending his competitive career, Moskvin began coaching in Dynamo club (Leningrad), then Burevestnik (Leningrad) and later Trud (Leningrad). He received the title of Honored Coach of the USSR.[7] His students included:
Many of his pupils later became coaches. Tamara Moskvina said that he was able to infect people with love for coaching.[2] When asked if there was a coaching rivalry between them, Moskvin said that he had never considered themselves rivals because he was more focused on singles while his wife was focused on pairs.[2]