Kendrick will start the second game of Tuesday's doubleheader against the Arizona Diamondbacks.
Castro was acquired from Toronto in the trade that sent Troy Tulowitzki to the Blue Jays. Castro was 2-0 with a 1.32 ERA in 11 appearances for Albuquerque.
Kendrick was placed on the DL on Aug. 1 with right shoulder fatigue. He has struggled in his first year with Colorado, going 4-12 with a 6.43 ERA in 21 starts this season.
Logan was 0-2 with a 4.75 ERA in 48 appearances before going on the DL on Aug. 14 with left elbow inflammation.