Southee faces an operation on Thursday and his World Cup fate will be decided early next week, but New Zealand coach Gary Stead is hopeful the bowler can recover in time.
"We've got our fingers crossed the surgery goes well for Tim," Stead said.
Southee, New Zealand's Test captain, will have pins or screws inserted in his thumb, Stead said.
"Providing the procedure is a success, it will be a matter of ensuring Tim can tolerate the pain and manage the actual wound when returning to train and play," Stead added.
The Black Caps coach hopes Southee plays in their World Cup opener against England in Ahmedabad on October 5th.
Southee suffered the injury last Saturday while dropping a catch off England's Joe Root in the final one-day international of the four-match series.
The New Zealander immediately looked to be in pain and left the field to go for a scan, failing to return.
The 34-year-old has taken 214 wickets in 157 ODIs.
"Tim's obviously a hugely experienced and important figure in our team. We want to give him every chance to be part of this World Cup campaign," Stead added.
New Zealand are bidding to reach a third straight final at the ODI World Cup.
