The team made the move before Sunday's game against the San Francisco Giants.
Anderson was the losing pitcher Saturday as the Giants won 8-4. He pitched 3 2-3 innings and allowed seven runs on 10 hits.
Manager Chip Hale said Anderson felt some soreness after his outing and is to undergo further medical tests.
''We just felt like it was a good time to give him some rest, get him back on track,'' Hale said.
Anderson is 4-4 with a 4.37 ERA in 18 starts this year. He is expected to miss at least two starts.