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India defeated West Indies by 88 runs in the fifth T20I having already sealed the series.
Iyer, who was preferred over the in-form Deepak Hooda, Sanju Samson and Ishan Kishan, fell for a four-ball duck in the opening T20I..
Andre Russell who scored an unbeaten 49, bagged 3/22 later.
KKR were bowled out for 101 runs chasing Super Giants total of 176/7.
Iyer, apparently unhappy with the way the chase panned out after his dismissal, is seen in an animated argument with head coach Brendon McCullum.
Sunday's victory over Sri Lanka was India's 12th successive T20I win, the joint-longest winning streak for a full member (the other being Afghanistan), and their seventh series win on the trot at home in this format.
Iyer would need to showcase all-round skills as that's what the team is looking for in the middle-order slot, skipper Rohit Sharma has said.
Iyer had previously captained Delhi Capitals in 2020.
The 10 teams in the league, following the addition of Gujarat Titans and Lucknow Super Giants, will be bidding heavily for the Indian players in a list of 590 cricketers, including 227 overseas candidates up for grabs during the two-day event.
Besides regular captain Kohli, who is missing the match owing to upper back spasm, middle-order batter Shreyas Iyer was also ruled out of the game due to a stomach bug.