The two-time world champion trained often with choreographer Nikolai Morozov, facility officials said.
The 25-year-old figure skater was reportedly stabbed in the right thigh by two men trying to steal his car's mirrors.
Ten won bronze at the 2014 Sochi Olympics in the men’s singles competition and was just the fourth Kazakh athlete to win a Winter Olympic medal.
In a tribute to Ten, the Ice House said not only was he an incredible athlete, but "most importantly, he was a nice guy."
"We are shocked and saddened to hear the news of his untimely passing and join the chorus coming from the skating community throughout the world in expressing our sincerest condolences and sympathy to his friends and family."
U.S. Olympic figure skater Adam Rippon remembered Ten as being kind to everyone.
"Denis, thank you for showing us how to be a champion," Rippon said in a Tweet. "Your time with us was way too short. Love you forever."
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