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The Badminton Association of Indonesia said in a statement that former player Candra Wijaya witnessed Kido collapse while playing badminton at a sports complex in Tangerang.
Kido has played badminton at the venue every Monday.
The doubles specialist won gold at the 2008 Beijing Olympics partnering Hendra Setiawan, a year after the pair won the men's doubles title at the world championship in Kuala Lumpur.
He also won the World Cup title in 2006 and Asian Games gold four years later, also partnering Setiawan.
PBSI chairman Agung Firman Sampurna said Kido's death is a "huge loss" for the Indonesian badminton family, which is currently preparing for next month's Tokyo Olympics.
On Saturday, Danish footballer Christian Eriksen collapsed suddenly on the field during a game against Finland and was revived. His doctor later confirmed he'd had a cardiac arrest.