Taibu played as a specialist batsman in Zimbabwe's 2-1 series defeat in the recently concluded one-day series as he battles a long-standing finger problem, while Chigumbura is nursing a knee injury.
Zimbabwe have beaten Bangladesh and lost to Pakistan since returning to Test cricket in August following an absence of more than five years from five-day cricket, and will be hoping to end their home season on a high.
'New Zealand are a quality side but we feel we have a bowling attack that can make inroads into their line-up,' said Zimbabwe captain Brendan Taylor.
'Daniel Vettori's arrival is a big boost for them, but we'll look to bat long and if we can take the game deep into day five then anything can happen.'
Left-arm spinner Vettori skipped the limited overs matches after announcing that he would take a break from the shorter forms of the game.
Taylor scored 310 runs in the one-day series - a record aggregate for a three-match series - and will hope to produce the same form in the Test match.
The hosts could hand a Test debut to Malcolm Waller, whose 99 not out in the third one-day international allowed Zimbabwe to complete their highest ever run chase, as they achieved a target of 329 in a dramatic finale.
