Manager Bud Black says converted outfielder Jason Lane will be recalled from Triple-A El Paso to make the fill-in start.
Black says Kennedy suffered the ''mild'' oblique strain in an at-bat.
Black said before Sunday's game Kennedy will miss the start despite being ''so close'' to being ready to pitch Sunday. Kennedy has been playing catch and is expected to start either Friday or Saturday.
Kennedy is 8-9 with a 3.66 ERA and has been mentioned in trade rumors.
Lane, who played outfield for Houston and the Padres from 2002-2007, threw 4 1-3 scoreless innings in two appearances with San Diego in June.