Navalny's supporters say Sobol rang the doorbell of an alleged FSB security service officer on Monday evening. Navalny previously accused the agent of taking part in a bungled plot to poison him with a nerve agent in August.
The FSB has dismissed the accusations by Navalny, who has said he would return to Russia hoping to capitalize on a higher profile in the wake of the poisoning case, which has raised tension between Moscow and Western capitals.
The move against Sobol is the latest in a clampdown on the Kremlin's opponents before next year's parliamentary election. Sobol has been seeking to run, although outspoken critics are often barred from standing.
Police took Sobol in for questioning on Friday. The Investigative Committee, which handles serious crime probes, announced on its website that it was launching a criminal case.
It said Sobol and several others had repeatedly tried to gain entry to an old woman's flat in eastern Moscow, wearing uniforms used by the state consumer health watchdog.
It said Sobol tricked a delivery courier to get into a block of flats and barged into the woman's flat when she opened the door, adding Sobol was suspected of using violence to illegally enter, an offense that carries a two years in jail.
Navalny, who is in Germany where he was treated after collapsing on a plane in Russia, condemned the action.
Germany and other Western nations say Navalny was poisoned with a Soviet-style Novichok nerve agent in a murder attempt. The Kremlin has repeatedly denied the accusations.