Potts has impressed for England's Test team this year after recovering from several injuries. The Durham fast bowler has played all four Tests under new captain Ben Stokes, taking 18 wickets at an average 26.72 during England's winning run against New Zealand and India.
Despite making just 10 List A appearances at domestic level, the 23-year-old has been handed his chance to take on the Proteas.
England, who face India in an ODI series decider at Old Trafford on Sunday, begin their next limited over series just 48 hours later at Potts' home ground of Chester-le-Street.
Another change sees first-choice leg-spinner Adil Rashid return for both the 50 and 20-over squads in place of Matt Parkinson, following his return from The Hajj pilgrimage to Mecca.