But Alviro Petersen will sit out the game after straining his hamstring, though he is expected to feature in next week's third Test at Lord's.
Smith injured his knee fielding in the deep at Headingley while Kallis sufered back spasms, though both were able to bat in the second innings.
Proteas team manager Dr Mohammed Moosajee said: "Graeme has fully recovered from the minor ligament sprain to his left knee and we also have positive feedback from Jacques, who has responded well to treatment following the acute back spasms that he suffered during the Test.
"Alviro is progressing well with rehab after the grade one hamstring strain he sustained at Headingley but he is unlikely to feature in the tour match against Derbyshire. He will be focusing on his rehabilitation with the aim of making sure he is fully fit for the final Test at Lords."
All-rounder Albie Morkel, who has been struggling with an ankle injury, has been made available for the two-day game but will play purely as a batsman.