Sobyanin's campaign representative, Lyudmila Shvetsov, says he will focus instead on "direct interaction with voters."
Shvetsova did not say what prompted the decision.
But reports from Moscow have suggested that Sobyanin is reluctant to debate opposition leader Aleksei Navalny.
Earlier this week, Navalny reported that Sobyanin's underage daughter owns a large apartment in central Moscow that the family could not afford on their publicly disclosed income declarations.
The Kremlin says the apartment was granted to Sobyanin when he worked in the presidential administration in the 2000s.
Navalny and four other opposition candidates are set for live debates on Moscow-owned radio and television, starting on August 12.