The selectors opted to include the two, who are yet to play one-day international cricket, with an eye to future commitments on the subcontinent.
Pakistan are hosting the Champions Trophy this autumn while the next World Cup, in 2011, will be co-hosted by India, Pakistan, Sri Lanka and Bangladesh.
And India are hosting South Africa for a Test series starting next month.
"Selectors were keen to try Amla in one-dayers and see how he fares. Also, we always wanted to try out two spinners in view of two key events to be hosted by the subcontinent," South African media manager Michael Owen Smith said.
"We wanted to expose Harris to the subcontinental conditions with an eye on the tour of India. We need to be fresh and ready for that challenge."
Off-spinner Johan Botha is the other spinner in the squad, playing their first ODI series since the retirement of pace bowler Shaun Pollock this month.
Veteran all-rounder Jacques Kallis, wicketkeeper Mark Boucher and paceman Makhaya Ntini are rested, with Graeme Smith continuing to lead the side.
There was speculation that Smith would be among the seniors who would fly back home after the second Test against Bangladesh beginning here on Friday, ahead of the three-Test tour of India.
But Owen said an experienced senior player was needed to guide the young team in tough conditions.
"With the likes of Kallis and Boucher out of the team, it was important to have some experience left. It is quite a young squad and some kind of experience is a must."
Smith will also play in the much-hyped Indian Premier League Twenty20 competition, slated to start on April 18.
Opener Herschelle Gibbs, who comes in for Neil McKenzie, fast bowler Charl Langveldt and all-rounder Vernon Philander are expected to join the squad on March 2.
The first one-day match will be played here on March 9, followed by the remaining two in Dhaka on March 12 and 14.
Squad: Graeme Smith (captain), Hashim Amla, Johan Botha, A.B. de Villiers, J.P. Duminy, Herschelle Gibbs, Paul Harris, Charl Langveldt, Albie Morkel, Morne Morkel, Andre Nel, Robin Peterson, Vernon Philander, Dale Steyn.