Dinamo confirmed the positive tests and said it was quarantining its team and staff to its training base as a precaution.
Forward Clinton N'Jie and midfielders Charles Kabore and Sebastian Szymanski were the positive tests, but all other players tested negative.
The game has been rearranged by the Russian Football Union for July 19.
The Russian league restarted on Friday after a a three-month hiatus. The meeting between Moscow and Krasnodar is the second game to be affected by the virus.
On Friday, FC Rostov was forced to field its youth players after an outbreak in its squad. Sochi refused to postpone the game and went on to win 10-1.
The man of the match award went to Rostov goalkeeper Denis Popov who, aside from conceding 10 times, managed to set a Premier League record by making 15 saves, including a penalty from Anton Zabolotny.
Zenit St. Petersburg are favourites for the title, but there is a battle ongoing for the other two Champions League spots allocated to the Russian league.
Krasnodar are third in the table while Rostov are fourth.