Iglesias was Cincinnati's scheduled starter against Atlanta on Wednesday. Mattheus was expected to report to Cincinnati on Thursday.
Right-hander Carlos Contreras was optioned to Louisville to make room on the roster for Iglesias, whose start against the Braves will be his second in the majors. He left with no decision against St. Louis on April 12.
Mattheus pitched in parts of four seasons with the Washington Nationals before signing with the Angels in January. He went 0-2 with a 2.84 ERA in 11 games this season for Triple-A Salt Lake and made one relief appearance for the Angels, allowing a walk with two strikeouts in one inning.
The 31-year-old Mattheus is 7-7 with a 3.58 ERA over 146 career appearances, all in relief.