Paramedics were called to a home in the upscale enclave of Coto de Caza just before 6:30 p.m. Saturday, said Capt. Tony Bommarito of the Orange County Fire Authority.
"Our little girl loved life and lived it to its fullest every day," Miller said.
Emmy was the youngest of the New Hampshire native's four children.
The death was under investigation, Orange County Sheriff’s Office spokeswoman Carrie Braun said.
Paramedics tried unsuccessfully to resuscitate the girl and rushed her to an emergency room, Bommarito said.
“They had no pulses the whole way,” Bommarito said. “It didn’t end well.”
The U.S. Ski and Snowboard Team tweeted its condolences to Miller and his family.
Miller is the most decorated male U.S. skier, with multiple World Cup wins. He won one gold, three silver and two bronze medals over three Olympic Games.
In his Instagram post, Miller asked for privacy for the family.
The Associated Press contributed to this report.