Krishna is set to join the India A squad for the third unofficial Test, also in New Zealand, while Nabi will link up with the 50-over squad for the series that starts on Wednesday.
According to a statement from the BCCI, Krishna "will need additional time to build up the workload required to be ready for matches."
Nabi has played a single international for India so far - the second ODI against West Indies in September, when he bowled a ten-over spell of 0 for 84.
India have already won the five-match T20I series, being 3-1 up with the final game to be played in Hamilton on Sunday.
New Zealand's bowling unit fought hard to defend a low total but India came out on top by four runs (DLS method) in the second ODI in Wellington as the visitors went 2-0 ahead in the five-match series.
Arshdeep Singh took four wickets before Virat Kohli hit 74 as India beat New Zealand by five wickets in a rain-affected first of five ODIs that was played in Auckland on Wednesday.
New Zealand claimed a morale-boosting seven-wicket victory over India in the fifth and final T20I in Hamilton on Sunday.
Glenn Phillips struck a century while seamer Jacob Duffy took four wickets as New Zealand claimed a consolation victory in the T20I series against India in Auckland.
