News agency Kazinform reported Mr Ten - who won bronze at Sochi 2014 - was stabbed in the thigh in Almaty on Thursday after two men tried to steal his car mirrors.
Mr Ten, a two-time World Championship medallist, was rushed to hospital but died three hours later of his injuries.
"Unfortunately, he is not with us anymore," a government spokesman said.
US figure skater Adam Rippon wrote on Twitter: "He was so kind to everyone and a huge inspiration to me and so many other people.
