Swann, 33, is one of a handful of players who represent England in all three formats and the ECB are keen to manage his workload ahead of another busy year on the international circuit.
The Nottinghamshire off-spinner has admitted to carrying a long-term elbow problem in his right arm and will take the next three matches off before returning for the three-game Twenty20 series.
Swann was one of England's better bowlers in Tuesday's defeat to the Proteas in the second one-day international, clean bowling Dean Elgar and AB de Villiers on his way to figures of two for 50.
Team director Andy Flower favours 30-year-old Tredwell as a like-for-like replacement for Swann and he has so far played one Test and six ODIs.
He will join the team for training at Kia Oval on Thursday and will compete with the likes of Samit Patel, Jade Dernbach and Chris Woakes for a place in the England XI.