Ministry spokesman Boris Malakhov said that if reports that authority and property is being handed over by the mission to the EU are confirmed, these moves would be in violation of UN Security Council Resolution 1244 and "must be stopped immediately".
According to media reports, the EU plans to deploy a 2,000-strong police and justice mission in Kosovo to eventually replace the UN mission.
The UN mission in Kosovo, stationed in the area since the end of an interethnic conflict in 1999, plans to reconfigure itself in the region after June 15, when Kosovo's government is due to take over from the UN.
Kosovo, with a 90% ethnic-Albanian majority, has been formally recognized as a sovereign state by 40 countries including the U.S. and most EU members since it proclaimed its independence from Serbia on February 17.
Russia, Serbia's long-time ally and a veto-wielding member of the UN Security Council, has refused to recognize Kosovo's independence.