Cardiff loose-head prop Rhys Barratt and Dragons back-row forwards Harri Keddie and Ryan Woodman all made their international debuts in Twickenham, but miss out on the squad for the three Tests.
Wings Gabriel Hamer-Webb and Tom Rogers, centres Bryn Bradley and Joe Roberts, fly-half Jarrod Evans, scrum-half Ellis Bevan, lock or flanker Freddie Thomas and back-row forward Olly Cracknell also miss out.
Leicester open-side flanker Tommy Reffell makes the cut after being overlooked by Tandy for the autumn internationals and Six Nations.
“We have selected a squad of 33 players for the Nations Championship to mirror what will be required for the World Cup in 2027,” said the head coach, who cut 11 players and lost Jenkins.
“We are building a lot of competition among our group of players, which is what we want to have, and there were some tough calls to make.
“We have an exciting opportunity over the next three weeks in a brand-new competition and can’t wait to get our campaign started against Fiji on Saturday.”
Louis Rees-Zammit, Max Llewellyn, Tomos Williams, Rhys Carre, Nicky Smith, James and Reffell could not face the Baa-Baas because they play for English clubs, but all return for the Nations Championship fixtures.
The loss of Jenkins means that Tandy is down to three specialist locks – Ben Carter, Teddy Williams and Adam Beard, who is included fresh from playing for Montpellier in their Top 14 final defeat by Toulouse on Saturday.
The former Ospreys second-row forward, who lost his starting spot to Carter during the Six Nations, came on in the final quarter in Paris.
“He has been with us for two campaigns, is battle-hardened and is really experienced,” said Tandy about Beard.
Wales had already lost centre Louie Hennessey, tight-head prop Keiron Assiratti and hooker Liam Belcher to injury before cutting down their squad.