It depends on what you mean by "real political influence", and while I fully understand that by "since Communism" your asking post-1991, I'm interpreting it as since 1917 (when the Bolsheviks took over). Using those parameters I would say that yes, there has been women in Russia since 1917 who fit that criteria, albeit not many.

One that comes to mind would be Nadezhda Krupskaya, the wife of Lenin. She was much more than just Lenin's wife, but an active revolutionary in her own right, and the argument could even be made that their marriage was more a political/revolutionary union than one of love (especially if one looks at the influence of Inessa Armand, a fellow revolutionary and purportedly Lenin's lover).

Since this is about post-1917, I won't get into what Krupskaya did before then, aside from mention she was very much an active participant in the Bolshevik movement, one of the main organizers of everything. After 1917 she took up major roles in government and party as well. Her main role in the Soviet Union was in education: after the October Revolution she took up a deputy role to Anatoli Lunacharsky, who was the People's Commissar for Enlightenment (Bolshevik for "Minister of Education"). In this role she was a major figure in adult education, and helped plan policy for education across the USSR as a whole. She held this role until her death in 1939.

Lenin became quite ill in 1921 and 1922, and as his wife she became the gatekeeper to access to him. This was important as Lenin was revered by the Bolsheviks as a whole, and as it became clear he was dying, a power struggle broke out to succeed him. Whoever could curry his favour was likely to come out on top, so with Krupskaya being the arbiter of who spoke to Lenin, and about what, she played a big role there. This was made most apparent at one time when Stalin, denied access to Lenin, said some unflattering things about Krupskaya. This made it's way to Lenin, who was furious about Stalin's remarks (it was about his wife, after all), and threatened to cut him off completely. Luckily for Stalin, Lenin did not have the strength to follow through, and died in 1924.

Krupskaya was able to keep going without Lenin though, and was promoted in 1924 and given a seat on the Central Committee, which was the main directorate of the Party (and de facto of the state). Despite her testy relationship with Stalin, she was opposed to Trotsky taking over leadership, and indirectly allied with Stalin to stop that from happening. As the widow of Lenin her voice carried weight, and while she wasn't directly with Stalin, it did contribute to his victory and assumption of power in 1929.

Outside of the party infighting, Krupskaya retained a leading role as an education advocate, and a major proponent of increasing literacy through the development of libraries in the USSR.

However by 1930 she had soured again on Stalin, and began to openly criticize him, but as the widow of Lenin, and as Stalin was not yet fully secure in his role, she was able to maintain her status, albeit given increasingly reduced roles, and became more of a matriarch for the Party and state as a whole. She died in 1939 aged 70, and was honoured as a major Bolshevik, despite her opposition to Stalin.