Colin de Grandhomme has been ruled out of the Test series against West Indies due to bone bruising to his right foot and left-arm spinner Ajaz Patel will miss the opening match as he continues to recover from a calf injury.
Santner has also been named captain for the third T20I against West Indies when Tim Southee, who was standing in for Kane Williamson, will depart the squad to link up with the Test team in Hamilton. Santner and Mitchell will join the Test squad on December 1, two days ahead of the start of the opening match.
"The unavailability of Colin and Ajaz has obviously had a flow on effect to our T20 squad who are providing the replacement players for the Test squad," New Zealand coach Gary Stead said. "I highlighted last week how tight and complex the schedule was - so when you throw in some injuries, it really begins to challenge how you juggle your resources.
"Mitch and Daryl will be available for the final T20 game, before linking up with the Test squad on Tuesday where we will monitor them closely to ensure they're fit and fresh ahead of the first Test on Thursday.
"I'd like to acknowledge Mitch Santner for taking on the responsibility to captain the T20 side. It's a great honour to lead your country and I know his calm demeanour along with the sheer amount of international experience he's amassed in the past five years will hold him in good stead.
"It's disappointing for Colin to be ruled out of the Tests completely and he'll now target being fit and available for the Boxing Day Test at Bay Oval. Ajaz will join the team in Hamilton to have treatment and train. We will make a call on the second Test in Wellington closer to the time."
Meanwhile, all the New Zealand and West Indies players who arrived from the IPL have cleared their third and final Covid-19 tests meaning they are on track to leave managed isolation on Thursday, the day before the opening T20I at Eden Park.