Earlier in the day, clashes broke out between the participants of the Immortal Regiment campaign and Ukrainian nationalists on Tuesday at the Eternal Flame memorial in Kiev.
"Forty five people were detained all across the country," Yarovoy told a briefing.
Earlier in the day, the police said that a group of people had blocked the entrance to the park that was to be the final destination of the march.
The "Immortal Regiment" is a patriotic initiative that commemorates WWII soldiers in marches held across Russia and other countries. Within the framework of the movement, people march with images of their ancestors, who had participated in World War II. For the first time, the rally took place in 2012, in Russia's Tomsk and then has spread to other cities and countries across the world.