The law on protection of children from harmful information that came into force in 2012 authorises regulators to block access to data deemed "harmful to the health and development" of children through promotion of suicide, porn and drugs.
Critics claim the law might be used as an Internet censorship means, but Russian authorities dismiss the claims.
The lawsuit filed in a Moscow court is against Rospotrebnadzor's decision to block access to a "video lesson on how to cut veins".
"In this case, we have appealed the decision of the Russian consumer watchdog because we do not believe that the goal of the law was to limit access to videos that are clearly intended to entertain viewers," the Wall Street Journal quoted Google as saying in a statement.
YouTube was briefly put on a blacklist of websites with harmful content in November 2012.
Media and communications watchdog Roskomnadzor said the website had "suicide promotion" materials.