Simmons, a pending free agent, told Maria Torres of the Los Angeles Times that concerns about COVID-19 prompted his decision.
"Major League Baseball and the Major League Baseball Players Association developed an environment and system that empowered players and provided us with the opportunity to decide on whether to play or opt out of the season. At this moment, I feel this is the best decision for me and my family," Simmons said in a statement. "We don't know what the future holds, but we would like to sincerely thank the Angels organization and Angels fans for welcoming (us) and making us feel at home."
The Angels said they "respect Andrelton's decision."
Manager Joe Maddon said he didn't speak to Simmons before he made his decision. Simmons didn't return a text message the skipper sent him during the bus ride to San Diego, according to Jeff Fletcher of the Orange County Register.
"I wish him well," Maddon said, according to Torres.
He added: "It's just unfortunate. He's a big part of what we're doing right now."
Simmons is in the final season of a seven-year, $58-million contract he initially signed with the Atlanta Braves in 2014. He was traded to the Angels before the 2016 season.
The 31-year-old slashed .297/.346/.356 in 30 games this year. His usually elite defense took a hit, with his minus-1 defensive runs saved serving as the first time in his career he failed to save at least 10 runs.
Simmons owns a career slash line of .269/.317/.379 with 67 homers, 406 RBIs, and 67 stolen bases over parts of nine seasons. A four-time Gold Glove winner and two-time Wilson Defensive Player of the Year, his 192 defensive runs saved are the most by any shortstop since he entered the league in 2012.