A CSA statement said Harris would miss the tour because of an abscess that required surgery.
"Robbie has shown excellent form in the (first-class) Supersport Series," selection chief Joubert Strydom said in the statement.
"He was the leading wicket-taker among South African spin bowlers with 24 wickets."
Peterson's call-up brings the number of black players in the 14-man squad to five.
The naming of the squad was delayed after the selectors and CSA president Norman Arendse became embroiled in a dispute over the number of black players who were chosen.
CSA's transformation policy sets a target of seven black players in squads of 15, and six in a squad of 14.
South Africa will play two tests and three one-day internationals in Bangladesh.