Kuokleva died on Tuesday night Swedish time and was 53 years old, among others the Russian state-controlled news agency RIA Novosti reported.
The death was later confirmed by the Russian Biathlon Federation.
"We announce with deep sadness that the Olympic champion and honorary athlete Galina Koukleva has passed away," the federation writes.
The Russian won three gold and two silver medals at the World Championships, including an Olympic gold medal in the sprint and a silver medal in the relay at the 1998 Nagano Games. That same year, Swedish biathlete Magdalena Forsberg was a strong favourite to become Olympic queen, but did not win a single medal.
Kuokleva also won several World Cup competitions. She ended her biathlon career in 2003.
