Southee dislocated and fractured his thumb while attempting to take a catch during a one-day international against England last month but was cleared to join the team in India having progressed well in his recovery.
New Zealand are also without regular skipper Kane Williamson (33) for Thursday's opener, which is a rematch of the 2019 final that England won. Williamson is recovering from a knee injury.
"No Kane and no Tim as well," Latham told reporters. "He's unavailable for selection just in terms of what happened to his thumb ... but he's recovering nicely.
"He's nearly two weeks post-surgery so fingers crossed he can keep recovering. It's a bit of a day-by-day process with him in terms of what that looks like.
"But fingers crossed he'll be available sooner rather than later as well."
Williamson's participation at the event was thrown into doubt when he underwent surgery for a torn anterior cruciate ligament in April but he has impressed with knocks of 54 and 37 in warm-up games against Pakistan and South Africa recently.
"It's great to see Kane back and to see him batting," Latham told reporters. "It's like he never left, to be honest, in terms of batting.
"It's great to see him moving really well too. He's playing all the shots he used to play.
"To see him back on the field is another stepping stone in terms of where he needs to get to in terms of his recovery."
Latham said his team would treat their first match at the 132,000 capacity Ahmedabad stadium like any other game.
"Leading into a game, there's always anticipation of what it's going to be like. But for us it's about trying to do what we do really well," Latham said.
"The good thing about this group is that we stay really level and we've done that for a long period of time.
"Even though it's a massive occasion for us ... it's just another game and if we do what we do well, we'll give ourselves a good chance towards the back end of the game."
