The Dragons also face four Nations League ties in June, with home and away games against Holland as well as a trip to Poland and a visit from Belgium.
Bale has made just two cameo substitute appearances for Real Madrid since scoring both goals in Wales' 2-1 World Cup play-off victory over Austria on March 24.
The 32-year-old has been absent from Real's last five matchday squads with a back problem.
But Bale has returned to training in the Spanish capital, and is on course to be available for Real's Champions League final date with Liverpool on May 28.
Aaron Ramsey is included after suffering penalty shoot-out misery for Rangers on Wednesday.
Ramsey featured for just the final three minutes of Rangers' Europa League final defeat to Eintracht Frankfurt in Seville, with his saved spot-kick proving decisive.
With Wales hoping to play at the World Cup for the first time since 1958, Leicester goalkeeper Danny Ward is available again after knee surgery and replaces Salford's Tom King.
Bournemouth forward Kieffer Moore also returns to the squad after missing the Austria win with a broken foot.
Moore helped secure the Cherries' return to the Premier League last month by scoring four goals in three matches.
Everton striker Nathan Broadhead, who has netted 13 goals in 26 appearances during an injury-hit loan spell at Sunderland, receives his first senior call-up.
MK Dons midfielder Matthew Smith comes in for Cardiff's Will Vaulks, while Swansea defender Ben Cabango misses out after suffering ankle ligament damage.
Huddersfield's Sorba Thomas and Nottingham Forest forward Brennan Johnson are set to miss the Nations League game in Poland on June 1.
Both players are involved in the Sky Bet Championship play-off final at Wembley three days earlier.
Wales squad: W Hennessey (Burnley), D Ward (Leicester), A Davies (Sheff Utd), C Gunter (Unattached), B Davies (Tottenham), C Roberts (Burnley), C Mepham (Bournemouth), J Rodon (Tottenham), N Williams (Liverpool), R Norrington-Davies (Sheff Utd), E Ampadu (Venezia, on loan from Chelsea), J Allen (Stoke), J Morrell (Portsmouth), M Smith (MK Dons), D Levitt (Man Utd), A Ramsey (Rangers, on loan from Juventus), J Williams (Swindon), H Wilson (Fulham), S Thomas (Huddersfield), R Colwill (Cardiff), B Johnson (Nottingham Forest), D James (Leeds), G Bale (Real Madrid), K Moore (Bournemouth), M Harris (Cardiff), R Matondo (Cercle Brugge, on loan from Schalke), N Broadhead (Sunderland, on loan from Everton).