The Republic host Russia in Dublin on Friday night, before travelling to Bratislava to take on Slovakia on Tuesday.
Murphy has made two substitute appearances for his country, and will provide backup for first-choice keeper Shay Given.
Republic squad in full: Shay Given (Manchester City), Keiren Westwood (Coventry City), Joe Murphy (Scunthorpe United), John O'Shea (Manchester United), Seamus Coleman (Everton), Richard Dunne (Aston Villa), Sean St Ledger (Preston North End), Greg Cunningham (Manchester City), Kevin Foley (Wolves), Paul McShane (Hull City), Kevin Kilbane (Hull City), Keith Andrews (Blackburn Rovers), Glenn Whelan (Stoke City), Darron Gibson (Manchester United), Paul Green (Derby County), Liam Lawrence (Portsmouth), Aiden McGeady (Spartak Moscow), Andy Keogh (Cardiff City), Damien Duff (Fulham), Keith Fahey (Birmingham City, Robbie Keane (Tottenham Hotspur), Kevin Doyle (Wolves), Shane Long (Reading)