Playmaker Iniesta was sidelined for a couple of weeks with a bruised knee while centre back Puyol hurt his left leg in last week's 4-1 first-leg triumph.
Midfielder Song and full back Montoya had calf and Achilles problems respectively and all four missed Sunday's 3-0 La Liga win at home to Malaga.
With the record King's Cup winners holding a comfortable lead, Barca coach Gerardo Martino has rested regulars Xavi, Sergio Busquets and Dani Alves for the game at the Nou Camp, the club said on their website (www.fcbarcelona.es).
Barca are on course to meet La Liga rivals Real Sociedad or third tier Racing Santander in the last four.
Sociedad have a 3-1 lead ahead of Thursday's return leg at their Anoeta stadium in San Sebastian but the Santander players have threatened to boycott the match in protest over unpaid wages and have demanded the cash-strapped club's president and board step down.
On the other side of the draw, holders Atletico Madrid lead Athletic Bilbao 1-0 before their trip to the Basque Country on Wednesday.
Real Madrid, who lost 2-1 to Atletico in last year's final, have the same advantage when they host Espanyol at the Bernabeu later on Tuesday.