Alexander Murakhovsky, since appointed health minister of the Siberian region of Omsk, did not return from a hunting trip on May 7, state news agency Tass reported on Sunday, citing a police spokesman.
A local authority had earlier spoken of the disappearance of a man born in 1971, without giving a name.
According to the report, additional police officers were requested for the search, dpa news agency reported.
Until a few months ago, Murakhovsky ran the Omsk clinic where Navalny, now jailed in a prison camp, was taken after he collapsed on a domestic flight last August.
Navalny was later flown out to Germany and treated for weeks at the Charite hospital in Berlin.
According to tests by several laboratories, he was poisoned with the nerve agent Novichok.
At the time, Murakhovsky did not diagnose a poisoning and said Navalny had fallen ill with a metabolic disorder.
Navalny accused him of falsifying the diagnosis, and his supporters accuse Murakhovsky of delaying his transfer to Germany at a critical time.
In November 2020, the doctor was promoted to health minister of the Siberian region.
Russia says it has not been able to prove that Navalny was poisoned and is therefore not investigating the matter.
The European Union and the US have repeatedly called on Russia to investigate the crime and imposed sanctions on the country.