Lopez was one of a dozen pop stars from around the world celebrating the leader's birthday at a Caspian Sea resort Saturday, the news agency said.
Other performers included Philipp Kirkorov, a Russian pop star of Bulgarian descent.
Lopez's visit to Central Asia was organized by China's National Petroleum Corp., which sends Turkmen natural gas to China, RIA Novosti reported.
Berdymukhamedov has led Turkmenistan since 2006. His rule has been described by Human Rights Watch as one of the world's most repressive regimes.