Warne broke the metacarpal bone in his hand while batting for English county side Hampshire against Essex but the injury is not as bad as it first appeared.
"Shane consulted with a hand specialist in England overnight and the pleasing news is that he won't require surgery," the Australian team doctor Trefor James said.
"In consultation with the medicos at Hampshire, we will be doing everything possible to speed his recovery but at this stage it appears as if he is a 50-50 prospect of being available."
Australia's chairman of selectors Trevor Hohns said Warne would be given every chance to prove his fitness but would be ruled out if he did not recover in time.
"As selectors all we can do is be guided by the advice of our medical staff," Hohns said.
"Shane will be doing everything he can to get himself right and we will give him as much time to do that as possible, but if he isn't 100 per cent fit then he won't be selected.
"At this stage though, no player has been placed on standby or nominated as a possible replacement for Shane. We just want to see how the injury progresses over the next few weeks before looking at that scenario."
Warne was set to be the main drawcard in Australia's two-Test series in Darwin and Cairns after Sri Lankan off-spinner Muttiah Muralitharan hinted he may pull out of the tour.
Muralitharan beat Warne in the race to pass Courtney Walsh as the world's leading wicket-taker but Warne was poised to overtake him when Australia's Test tour of Zimbabwe was suddenly cancelled.
Muralitharan said he was considering skipping the tour to give himself a short break after the controversy over his bowling action.
That would have presented Warne with a golden opportunity to move ahead of the Sri Lankan until he was struck on the hand by former England paceman Darren Gough.
Warne currently has 517 Test scalps, two behind Walsh and 10 less than Muralitharan.
