The team vice-captain sustained the injury while fielding during their 36-run victory over South Africa in the fourth game of the tournament at Warner Park on Saturday, reports CMC.
Subsequent X-rays revealed on Sunday that the damage would keep the left-hander out of action for up to six weeks, or could even require surgery.
"The X-Ray showed an intra-articular fracture of the distal phalanx of the index finger of the left hand - the top part of that finger," team doctor Geoffrey Verrall said on Sunday.
"We will assess the situation over the coming days to see if the injury requires a surgical option but should that not be the case then David is likely to be available to return to play in somewhere between two and six weeks."
A decision will be taken on if Warner will remain on tour and whether or not a replacement will be summoned.
Warner, who struck 109 in Saturday's game, said he would try to take the positives from the injury layoff.
"It's obviously disappointing to be sidelined given the form I've been in and given the important stage the tri-series is at, but it's always important to look at the positives," he said.
"This downtime, however long or short it is, will give me the chance to freshen up and spend quality time with my family after an intense period of action, with trips to New Zealand and South Africa, plus the World Twenty20 and the Indian Premier League."
And while Warner will be a huge loss to the Australia batting department, head coach Justin Langer said it was an opportunity to other players to step up.
"It's doubly disappointing to have David Warner sidelined because of his outstanding form plus his attitude and professionalism around the group which has been a joy to work with," Langer noted.
"But we've spoken from day one of this tour about every single person in the squad contributing to our success. I've encouraged the players not in the starting eleven to be ready at all times because you never know when opportunities might come. One of the boys will now get that opportunity in David's absence."