The right-hander, who was diagnosed with a non-displaced radial head fracture, is expected to miss at least four weeks.
Weaver left Sunday's loss against the Texas Rangers early after jamming his non-throwing arm while dodging a line drive. He was initially said to have suffered a strained elbow.
The Angels called up right-hander Dane De La Rosa from Triple-A Salt Lake to replace Weaver on the roster.
De La Rosa was acquired in a trade last month from Tampa Bay in exchange for right-hander Steven Geltz.