Mitchell Marsh, who was supposed to tour England with the Australia A team, has been flown in early as cover.
A final decision on Stoinis' future in the World Cup will be made after he is assessed again in the lead up to Australia's next game, against Sri Lanka on Saturday at The Oval.
The tricky part is to assess how long Stoinis will be out for: if a replacement is approved for a player, he cannot come back into the tournament unless there is another injury in the squad. Now, in the absence of a like-for-like all-rounder in the squad, Australia will have to decide if they can do without Stoinis for the period it takes for him to recover.
Stoinis sustained the injury during his fifth over against India at The Oval on Sunday, after which he came back for a two-over spell at the death. He bowled the 48th and the 50th overs, which involved a sharp return catch to dismiss MS Dhoni. "He was in some discomfort," Finch said of that spell.
"And it wasn't ideal, but he still managed to bowl a couple of overs. And speaking to guys who have done a side before, they say you can generally get through a game towards the end, but it's tough to get going after you've cooled down."
Finch said there will be a comprehensive assessment before a decision is made either way. "Not exactly sure on how many games he'll miss," Finch said.
"That's why Mitch is flying over. It's still being assessed. And over the next couple of days we'll have a clearer picture of what that looks like.
Mitch was meant to fly over with the Australia A side on Friday. He's just coming a couple of days early as a bit of precaution, if Stoinis doesn't recover quick enough or doesn't respond to treatment well enough over the next few days."
In the immediate aftermath, Australia will have to decide whether they go in with an extra batsman or bowler for the match against Pakistan. "We're going to have to juggle around especially that allrounder spot," Finch said.
"We've got to find a few more overs now, whether we play the extra batter or extra bowler, we'll wait and see, and especially tomorrow with the conditions."
Shaun Marsh had a long hit in the nets, which could suggest more bowling work for Glenn Maxwell, and potentially a few overs from Steven Smith and Finch himself. The other way to go about it might be to include Jason Behrendorff and push Alex Carey, Nathan Coulter-Nile and Pat Cummins a spot each in the batting. AGENCIES