The Phillies placed Billingsley on the 15-day DL because of a strained right flexor tendon after the team's 5-3 victory over the Tampa Bay Rays.
Amaro later told reporters Billingsley's arm was sore, and the root of the problem could be a nerve issue.
Billingsley left Saturday's start after five innings. He missed most of the past two seasons after two elbow surgeries.
Billingsley, 83-64 with a 3.72 ERA in his career, is 2-3 with a 5.84 ERA in seven starts in 2015, after he spent his first eight seasons with the Los Angeles Dodgers.
Information from The Associated Press was used in this report.