The Russian Football Union (RFU) announced the decision following an executive committee meeting on Tuesday.
It comes after the number of confirmed cases of coronavirus in the country reached 93.
An RFU statement on Tuesday said all matches under their control between March 17 and April 10 would be suspended.
These include the Russian Premier League, the Russian Cup and regional divisions.
League leaders Zenit had been due to face CSKA Moscow away from home on Sunday.
They are nine points clear at the top of the table after 22 rounds of matches.
CSKA Moscow, Krasnodar, Lokomotiv Moscow, FC Rostov, Rubin Kazan, Spartak Moscow and Zenit are the teams who have been suspended.
On Monday, FIFA responded to Russia's invasion of Ukraine by banning all of the country's national teams and club teams from their competitions. Russian clubs, similarly, have been banned from UEFA tournaments. St Petersburg had already been stripped of this season's Champions League final.
Now the ECA has followed suit, with the seven clubs ceasing to have any involvement with the organisation until further notice.
A statement released by the ECA following a meeting held at Tottenham Hotspur Stadium on Monday read: "Over the past week, ECA has acted swiftly and firmly in both endorsing and participating in the decisions of UEFA to suspend all Russian clubs from participating in UEFA competitions, together with UEFA's decision to end its commercial partnership with Gazprom.
"ECA also strongly endorsed the decision of UEFA's executive committee to move the Champions League final.
"In addition, today, the executive board specifically resolved that all Russian members will cease to be involved in ECA activities with immediate effect until further notice."
