Wilson, 33, has allowed 19 runs and posted a 10.26 ERA over his last four starts. He yielded six runs over 3 2/3 innings Wednesday night against the Blue Jays.
"Naturally, when a pitcher like C.J. goes the wrong way for so long, you're concerned," Manager Mike Scioscia said.
The two-time All-Star dealt with several injuries early in his career -- he underwent Tommy John Surgery in 2001 -- but has made at least 33 starts in each of the last four seasons.
Over 116 1/3 innings this season, Wilson has recorded a 4.33 ERA and 8-6 record with 107 strikeouts and 48 walks.
Angels right-hander Jared Weaver is also dealing with a back injury.
The Angels lead the American League Wild Card race by four and a half games but opened Thursday three and a half games back of Oakland in the AL West.
- Chris Johnson