A number of fans were arrested before the game by riot police, including in the city's subway system.
"In the main, those detained were young people under the influence of alcohol," he said.
The match at the Luzhniki stadium in the southwest of the capital was attended by some 60,000 fans, and saw Spartak Moscow defeat CSKA 1-0. The win was the first time the club had beaten their cross-town rivals for seven years.
After the game, as the Spartak players threw their shirts into the crowd, a number of fans fell into the space between the running track and the stands. Around 40 of them were injured. A small number of them suffered broken bones, but in the main the injuries were minor.