The left-arm offspinner fractured the thumb of his non-bowling hand playing for the Brisbane Heat in the Big Bash League last week and underwent surgery.
The injury forced Kuhnemann to miss Australia's ongoing training camp at the ICC Academy in Dubai, instead remaining in Australia to allow his surgical wound to heal.
Kuhnemann has since resumed bowling and Cricket Australia confirmed on Friday afternoon he would fly to Sri Lanka to meet the squad this weekend.
Kuhnemann will be joined by up-and-coming Victorian batter Oliver Peake, who has been invited to the squad's camp in Galle as a development player.
The 18-year-old has represented Australia at under-19s level and made his BBL debut for the Melbourne Renegades against the Heat last week, scoring 19 runs.
Kuhnemann's recovery is a big boost for an Australian squad looking for a rare subcontinent Test series win, with the left-armer a favoured selection option next to right-handed Nathan Lyon and Todd Murphy.
The 28-year-old made his Test debut on the last subcontinent tour to India in 2023, playing three of a possible four Tests and taking a five-wicket haul in the first innings of Australia's win in Indore.
But Kuhnemann's return to fitness looms as a blow to Cooper Connolly's hopes of making a shock Test debut in the two-match series that begins on January 29.
Cooper Connolly was named in the Australian squad, but is unlikely to be given a Test debut yet. (Richard Wainwright/AAP PHOTOS)
Connolly has played only four first-class matches and is yet to take a wicket at that level, but a series-ending injury to Kuhnemann would have left him as the sole left-arm spinner touring.
The 21-year-old now appears unlikely to earn a Test debut after a breakout 2024 that saw him earn maiden Twenty20 International and one-day international caps.
Kuhnemann's recovery comes after stand-in captain Steve Smith overcame a minor elbow injury to join the squad in Dubai this week.
Elsewhere, Cricket Australia has appointed Adam Griffith its new national pace bowling coach to help prepare for life after its golden generation of quicks.
Pat Cummins is the youngest of the so-called "big three" Test pacemen at 31 with fellow national mainstays Josh Hazlewood and Mitch Starc both 34.
Back-up options Scott Boland (35) and Sean Abbott (32) are also closer to the end of their careers than the start.
Griffith has left his role as an assistant coach at Cricket Victoria to take up a post that will have him mentoring the next generation of pacemen.
A member of the first Tasmanian team to win the Sheffield Shield in 2007, Griffith will not take part in the Sri Lankan tour; his role is mostly based at CA's National Cricket Centre in Brisbane.
Former Tasmania head coach Griffith has previously worked as a bowling coach for the Australian team on tours in 2012 and 2016, as well as at the 50-over World Cup in 2019.
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