A release from Cricket South Africa said that while Duminy had made the squad, he "will not play the first two matches but should be available for selection for the third." In Duminy's absence, Faf du Plessis, who had been rested for the T20s in Australia, will lead the side.
South Africa have also recalled wicketkeeper-batsman Morne van Wyk, in place of the injured Quinton de Kock. Van Wyk has not played an international game since the 2011 World Cup.
Duminy had captained South Africa during their last T20 series, against Australia in November, but picked up a knee injury which ruled him out of the subsequent ODIs on that tour, as well as the home Tests against West Indies.
Phangiso was also included in the squad for that Australia tour, but did not play a single game due to a finger injury. He last played for South Africa in September, going wicketless in the final of the Zimbabwe Triangular ODI series, against Australia in Harare.
The selectors have stuck with the young trio of Reeza Hendricks, Rilee Rossouw and Kagiso Rabada, who all made their international debuts in Australia last month.
"Once again we are resting a number of senior players who are involved across all three formats," Andrew Hudson, Cricket South Africa's selection convener, said. "This will be the last chance to rest them before we get into World Cup mode with the Momentum ODI Series against the West Indies."
South Africa will play the first of three T20 matches against West Indies on January 9 in Cape Town.
South Africa T20 squad: Faf du Plessis (captain), Kyle Abbott, Farhaan Behardien, Marchant de Lange, JP Duminy, Reeza Hendricks, Imran Tahir, David Miller, Wayne Parnell, Aaron Phangiso, Kagiso Rabada, Rilee Rossouw, Morne van Wyk, David Wiese