Medvedev's decree was published on the ministry's web site (www.mid.ru) on Tuesday.
Kislyak, a career diplomat who was Russia's envoy to NATO in 1998-2000 after heading the ministry's security and disarmament section, will replace Ambassador Yuri Ushakov, who has moved to a senior government post.
Earlier this month Kislyak led the Russian team in Geneva during inconclusive talks with Iran and six world powers — the United States, Russia, Britain, France, China and Germany.
The West suspects Iran of seeking to develop its own nuclear weapons and wants Tehran to stop enriching uranium for its atomic energy program. Iran denies any such plans.
Russia, which is building a nuclear power plant in Iran, sides with the West in pressuring Tehran to make its nuclear program transparent and in calling for a stop to uranium enrichment.
Russia has backed mild sanctions against Iran in the United Nations, but resists stronger moves, saying that trying to push Iran into a corner could only make things worse.
Differences over Iran are part of growing problems in Russian-U.S. relations that Kislyak will have to handle.
Washington plans to deploy elements of a missile defense system in Eastern Europe to avert potential Iranian ballistic strikes.
Russia says Iran does not have the missile capacity to threaten the U.S. and accuses the Washington of encroaching its national security.
(Writing by Oleg Shchedrov; Editing by Richard Balmforth)
