Maphaka’s injury follows the absence of first-choice fast bowlers Kagiso Rabada and Lungi Ngidi, who also have hamstring problems.
Lizaad Williams has been called into the squad as a replacement for Maphaka.
South Africa are also without seamers Ottneil Baartman (hamstring) and Nandre Burger (back), leaving their seam attack decimated.
Instead, they will rely on Williams, the Jansen twins, Marco and Duan, Gerald Coetzee, Corbin Bosch and Nqobani Mokoena.
Between them, the six have played only 72 ODIs in what will be one of the least experienced bowling line-ups for South Africa against a major opponent in some time.
The first match in the series will be played in Durban on Thursday, before further fixtures in Johannesburg on Sunday and Potchefstroom on September 30.