Harvey gave up eight runs on seven hits, including four home runs, in just 2⅔ innings against the Minnesota Twins on Thursday.
The 30-year-old deemed the "embarrassing" loss one of the worst starts of his career, but did not blame his struggles on an injury immediately following the game.
Harvey's agent, Scott Boras, told The Los Angeles Times on Saturday that the righty developed a muscular issue in his upper back during his start Thursday, but said it was "not anything long term."
Angels manager Brad Ausmus also told reporters Saturday that Harvey's back started acting up during the start, but said Harvey kept the injury to himself.
Harvey signed a one-year, $11 million deal in the offseason. His 7.50 ERA would rank highest among American League starters, though he doesn't have enough innings pitched in his 10 starts to qualify among the leaders.
Garcia returns after going on the injured list May 13 with a lumbar spine muscle spasm.
Cole was sent down to Salt Lake only Friday.
The Associated Press contributed to this report.