Trapattoni has recalled the Newcastle United winger Damien Duff, who missed the games against Georgia and Montenegro because of injury.
Murphy will be part of the Republic squad that will play Nottingham Forest in a friendly against Nottingham Forest on Thursday night, but he will return to Scunthorpe to play against Crewe Alexandra on Saturday.
After that game he will return to Ireland for the game against Cyprus, though with Shay Given and Dean Kiely also in the squad he is unlikely to feature.
The former Scunthorpe forward Andy Keogh is also included in the squad.
Ireland squad: Shay Given (Newcastle United), Dean Kiely (West Brom), Joe Murphy (Scunthorpe United), Alex Bruce (Ipswich Town), Damien Delaney (QPR), Richard Dunne (Manchester City) , Kevin Kilbane (Wigan Athletic), Joey O'Brien (Bolton Wanderers), John O'Shea (Manchester United), Paul McShane (Sunderland), Stephen Hunt (Reading), Aiden McGeady (Glasgow Celtic), Damien Duff (Newcastle United), Liam Miller (Sunderland), Andy Reid (Sunderland), Glenn Whelan (Stoke City), Kevin Doyle (Reading), Robbie Keane (Liverpool), Andy Keogh (Wolves), Shane Long (Reading), Daryl Murphy (Sunderland).