The team announced the moves before its game at the Astros on Tuesday.
Jordan is 0-3 with a 5.61 ERA in 25 2-3 innings over five starts this season. On Sunday, Jordan allowed one run in four innings and left with the score tied 1-1 in what became a 4-2 loss to San Diego.
In his previous start, on April 22, Jordan gave up the 499th and 500th homers of Albert Pujols' career.
Mattheus has a 5.40 ERA in 10 innings across eight appearances at Syracuse in 2014. He has a 3.77 ERA over three major league seasons.