In other cities, such as Samara and Stavropol, classes were temporarily suspended after receiving bomb threats via email.
Hundreds of schools were affected across the country.
According to the report, nothing suspicious was found during inspections.
Russia has had to deploy police in response to such threats repeatedly over the years.
Schools, courthouses and shopping centres are often targeted.
Authorities do not know what the motive might be in this most recent case.
The threats are mainly received by email.
The Russian domestic intelligence service FSB has already blocked foreign mail providers, suspected to be used to send the threats.
According to media reports, the mayor of Yekaterinburg in the Urals, Alexei Orlov, said that the threats were received at 3am.
He therefore assumed that the emails were sent from abroad.
In the city, 151 of the 163 schools were evacuated on Wednesday, according to the authorities.
Many schools in Moscow have already had drills for quick evacuations in case of an emergency.
