The left-arm offspinner ran from the ground in agony on Thursday night after attempting to field a Matthew Wade straight drive off his own bowling.
The injury occurred to his non-bowling right hand but appeared to be significant and left Heat and Test teammate Marnus Labuschagne visibly distressed post-game.
"I just heard about Matt Kuhnemann, so that's pretty bad," he told AAP.
"Thumb ... it doesn't look great. I really feel for him."
The 28-year-old is due to fly out to Dubai for a pre-Test training camp alongside Labuschagne on Sunday.
His absence would increase the prospect of a shock debut for allrounder Cooper Connolly.
The West Australian left-armer spins the ball away from the right-hander like Kuhnemann and is highly rated by Steve Smith - interim captain in Sri Lanka - despite not yet owning a first class wicket.
Right-arm off-spinners Nathan Lyon and Todd Murphy are already part of the touring party.
Uncapped West Australian off-spinner Corey Rocchiccioli, NSW leg-spinner Tanveer Sangha and Swepson are among those pushing for a late call-up to the squad if Kuhnemann is ruled out.
Kuhnemann played three Tests in Australia's 2023 tour of India, his style proving effective in sub-continental conditions as he claimed nine wickets, including 5-16 in the second Test.
Starved of Sheffield Shield opportunities given he was stuck behind leg-spinner Mitchell Swepson at Queensland, Kuhnemann opted to move to Tasmania this season.
It paid off, his 18 wickets in six games the most of any spinner in the competition as he pressed his case for a spot in the XI in Galle later this month.
"It's someone I'm close to and he's grown so much with his bowling and in Sri Lanka, he's probably one of the first picked over there," Labuschagne said.
"I'm really gutted."
Labuschagne tuned up for the tour with a BBL-best 77 from 44 balls, anchoring the innings before Hobart chased down their 201-run target on the final ball.
"I'm pretty confident, clear on my plans for how I'll go about it," he said of the spin test awaiting.
"So it's about cleaning that up in Dubai first.
"You can't put your finger down on one thing; you need different options because in the subcontinent, you hit one good sweep and there's two or three guys out there
"So you trust your defence, trust your sweep and your game and mix it all together."
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