The move is retroactive to May 3.
"I'm not injured,'' he said. "It's just recovering less and less each week, and the thinking is, miss two starts now and save missing five or six in the future.''
Padres manager Bud Black said the shoulder remained troublesome and the team decided to give him a full two weeks to rest. Morrow is 2-0 with a 2.73 ERA on the season.
Left-hander Frank Garces, who opened the season with the Padres, was recalled from Triple-A El Paso. He's 0-0 with a 1.59 ERA in six big league appearances.
The Associated Press contributed to this report.