"It's a real shame for Daryl to suffer this injury on the eve of an exciting period of cricket," the coach said. "Daryl's become a really important player to our T20 unit and we're certainly going to miss his all-round skills and versatility in the tri-series.
"With our first game of the World Cup in just over two weeks, we need to take some time to consider Daryl's recovery timeline and his potential involvement."
Mitchell was a standout while opening the batting during New Zealand's run to the final of last year's T20 World Cup, with their defeat by Australia coming after Devon Conway had suffered a broken hand in the semifinal win over England.
Conway has since assumed that opening role while Mitchell is now an integral part of the Black Caps' middle order, forming with Glenn Phillips and Jimmy Neesham a powerful closing trio.
Stead and co will at least have the next week to mull over their options to fill the hole left by Mitchell, with Michael Bracewell, Mark Chapman and Finn Allen the other batting options in the World Cup squad.
Bracewell has played only eight T20 internationals, all since July, but boasts impressive domestic numbers in the format, averaging 32 with a strikerate of 135 in 109 matches. The 31-year-old also offers a bowling option with his offbreak, but Mitchell's medium pace is unlikely to have been seen as an important cog in Australia.
Chapman, 28, has played 15 T20Is for New Zealand and averaged 25 with a strikerate of 140, while 23-year-old Allen has shown his shot-making ability while opening during a 13-match international career.
Any change is less than ideal for a Black Caps side who had been essentially content with their first-choice XI, though there are also still slight concerns over the health of Lockie Ferguson.
Stead said the paceman had a "little ab injury" the team were managing, possibly limiting his involvement in the tri-series. Adam Milne, Ferguson's competition for the third seamer spot, has looked good in the nets this week while recovering from an injury of his own.
Pakistan won the opening tri-series match this afternoon, with Mohammad Rizwan's 78 not out off 50 balls leading them to 167-5, with Bangladesh falling 21 runs short in reply.
The White Ferns, meanwhile, completed a 4-1 T20 series victory over the West Indies this morning, with Maddy Green scoring the winning run off the final ball as the tourists chased down 102 with five wickets in hand.