But, Arthur conceded Warner probably won't make an appearance in any of the five one-day internationals against the West Indies, starting on Friday in Perth.
Warner, 26, was cracked on the hand in the nets by fiery quick Mitchell Johnson during a training session at the WACA Ground late on Wednesday afternoon.
Scans later revealed a fracture in the belligerent batsman's left thumb.
Australia is likely to open against the Windies with wicketkeeper Matthew Wade in Warner's absence, while comeback kid Phil Hughes will remain at number three.
Usman Khawaja replaced Warner in the Aussie side and will likely slot in at number six behind George Bailey.
Arthur said while Warner isn't expected to line up against the Windies, the injury lay-off was unlikely to extend as far as the four-Test series against the Indians, which begins in Chennai on February 22.
"At this stage, we're still waiting on further medical advice, we don't think it'll be that long," Arthur told Perth talkback radio 6PR on Wednesday night.
"We think he should be right for India, which is not a bad thing."
Warner has already been ruled out of the first two clashes with the West Indians, with officials declaring he would be reassessed ahead of the third match in Canberra.
But the Australian coach went even further to suggest the possibility of a Warner return for the series was remote.
"He'll probably miss all five ODIs, though," Arthur conceded.
"That's not great at all, unfortunately, but it's something that happens and we had to have a plan in place quickly and we've acted on that."