Asked whether the assailant shouted anything, Mr Zhdanov said: “Everything happened in silence.”
“Of course this is a clear political attack, there is no doubt here”.
Lithuanian police said they had been informed a man was beaten outside his home and were investigating.
The alleged assailant is unknown, as is their motive.
Police fenced off a pine forest near Mr Volkov’s house on Vilnius’ northern outskirts. Officers with dogs and flashlights were seen searching it late on Tuesday night.
A large part of Navalny’s political vehicle, the Anti-Corruption Foundation, which includes Mr Volkov, are residing in European Union and Nato member Lithuania after fleeing Russia.