Opinion polls indicate Sobyanin will handily win a majority of votes, with Navalny earning about 20 percent.
Navalny is campaigning under the burden of a five-year prison sentence. The 37-year-old opposition leader, who has exposed alleged government corruption, says the charges are politically motivated and intended to silence him.
Navalny received his sentence in July, leaving the courtroom in handcuffs. A day later he was suddenly released, pending appeal.
Navalny, who has been blocked from state-run television, has conducted a Western-style campaign, mobilizing the support of thousands of volunteers.
By contrast, Sobyanin has been all but invisible throughout the campaign. He has instead focused on sprucing up the city of Moscow. Analysts say his campaign strategy is designed to remind voters of his access to the Kremlin and its money.