The Hundred is a new tournament consisting of eight city-based franchise sides, breaking away from England's traditional county system.
The 35-year-old said he needed to take "a step back" from the captaincy in order to help the emergence of the next generation of leaders under Quinton de Kock.
The decision of the Board of Control for Cricket in India (BCCI) follows January's meeting with a Cricket Australia delegation led by chairman Earl Eddings.
Morgan slammed seven sixes in an innings of 57 not out off 22 balls as England chased down South Africa's 222 for six with five wickets and five balls to spare.
The 16-member squad named Sunday has four changes from the team that lost to Pakistan by an innings and 44 runs in Rawalpindi.
Zimbabwe, playing their first Test series in more than a year, pushed Sri Lanka hard in two home matches in January before narrowly going down 0-1.
Bjorn Fortuin, playing his first innings in a T20 international, tried to flick the last ball from Curran to fine leg but was caught by Adil Rashid, running back from the edge of the 30m circle.
Opener Kamran Khan scored 68 in 52 balls to be adjudged the Player of the Match.
England's two-run win in a high-scoring match, punctuated by 30 sixes, levelled the three-match series, which will be decided in the third and final match in Centurion on Sunday.
Fixture congestion rather than security concerns was behind South Africa's decision to postpone a short tour of Pakistan.
Match-fixer Sanjeev Chawla, one of the central figures in the scandal surrounding the late Hansie Cronje, was sent back to India on Thursday after spending four years fighting extradition.
The last time the pair played in South Africa, almost two years ago, they were sent home in disgrace for attempting to alter the ball with sandpaper during a Cape Town Test.
Cricket Australia announced he will be replaced by D'Arcy Short in both formats.
Lancashire opener Jennings and Surrey wicketkeeper-batsman Foakes were discarded after the West Indies tour 12 months ago.
A KL Rahul century was not enough to save the tourists, who scored a respectable 296 for seven after losing the toss and being asked to bat.