Tandy initially named a 48-strong squad with six uncapped players including Exeter back rower Kane James and Harlequins centre Bryn Bradley, Dragons back-row duo Ryan Woodman and Harrison Keddie, Cardiff loose-head prop Rhys Barratt and Ospreys tight-head Ben Warren.
There were recalls for Dragons prop Dillon Lewis, Leicester flanker Tommy Reffell, Scarlets centre Joe Roberts and Cardiff scrum-half Ellis Bevan.
British and Irish Lions flanker Jac Morgan, Cardiff lock Teddy Williams and centre Max Llewellyn were included after missing the Six Nations because of injury.
The squad has since been cut by two players after Bath back Louie Hennessey and Cardiff prop Keiron Assiratti pulled out because of injury.
Tandy has had access to players at different times with the Welsh sides all finishing their domestic campaigns by the end of May.
However, the 13 players from English and French-based clubs are unavailable for the Barbarians game because the match falls outside World Rugby’s international window.
Morgan, Dewi Lake and Aaron Wainwright – who will link up with English clubs next season – are available to play.
The Baa-baas, who will have George North in their side against Wales, lost 80-31 against South Africa last Saturday.
After the Barbarians game, the Wales squad will be reduced further for the Nations Championship.
Forwards (26): Rhys Barratt, Rhys Carre, Nicky Smith, Gareth Thomas, Liam Belcher Ryan Elias, Dewi Lake, Evan Lloyd, Dillon Lewis, Sam Wainwright, Ben Warren, Adam Beard, Ben Carter, Dafydd Jenkins, Freddie Thomas, Teddy Williams, Ryan Woodman, James Botham, Olly Cracknell, Kane James, Harrison Keddie, Alex Mann, Jac Morgan, Taine Plumtree, Tommy Reffell, Aaron Wainwright.
Backs (20): Ellis Bevan, Kieran Hardy, Reuben Morgan-Williams, Tomos Williams Sam Costelow, Dan Edwards, Jarrod Evans, Bryn Bradley, Ben Thomas, Joe Hawkins, Eddie James, Max Llewellyn, Joe Roberts, Josh Adams, Mason Grady, Gabriel Hamer-Webb, Ellis Mee, Blair Murray, Louis Rees-Zammit, Tom Rogers.