The 23-year-old rugby league convert, who was born and raised in New Zealand, qualifies for England on residency grounds.
Solomona is one of 15 uncapped players in the squad, which will be captained by Dylan Hartley after he was left out of the British and Irish Lions squad.
On the tour, England will face their hosts in San Juan on Saturday, June 10, and in Santa Fe a week later.
England squad for June's tour of Argentina
Forwards: Will Collier (Harlequins), Luke Cowan-Dickie (Exeter Chiefs), Ben Curry (Sale Sharks), Tom Curry (Sale Sharks), Charlie Ewels (Bath Rugby), Ellis Genge (Leicester Tigers), Dylan Hartley - captain (Northampton Saints), James Haskell (Wasps), Paul Hill (Northampton Saints), Nathan Hughes (Wasps), Nick Isiekwe (Saracens), Joe Launchbury (Wasps), Matt Mullan (Wasps), Chris Robshaw (Harlequins), Sam Underhill (Ospreys/Bath Rugby), Harry Williams (Exeter Chiefs), Tom Wood (Northampton Saints)
Backs: Mike Brown - vice-captain (Harlequins), Danny Care - vice captain (Harlequins), Joe Cokanasiga (London Irish), Nathan Earle (Saracens), George Ford - vice captain (Bath), Piers Francis (Auckland Blues/Northampton Saints), Sam James (Sale Sharks), Alex Lozowski (Saracens), Harry Mallinder (Northampton Saints), Joe Marchant (Harlequins), Jack Maunder (Exeter Chiefs), Jonny May (Gloucester), Henry Slade (Exeter Chiefs), Denny Solomona (Sale Sharks)