Giovanni Trapattoni's side host Russia on Friday October 8, before heading to Slovakia the following Monday.
He will not miss any Iron games as the Championship is on an international break.
Murphy is expected to provide backup to the Manchester CIty keeper Shay Given, who is his country's undisputed No.1.
The Republic opened their qualifying with two wins, and Trapattoni is confident of further wins next month.
"We go into these qualifiers with six points from six, We performed well against Armenia and Andorra and we will build on these good results," he said.
"These teams are the top seeds in the group and they will be looking to take three points from us to kick start their campaigns but we have prepared well and will not make it easy for them as we continue to lay the foundations to qualify for the European Championship finals."
Full squad: Shay Given (Manchester City), Keiren Westwood (Coventry City), Joe Murphy (Scunthorpe United), John O'Shea (Manchester United), Richard Dunne (Aston Villa), Sean St Ledger (Preston North End), Greg Cunningham (Manchester City), Kevin Foley (Wolves), Stephen Kelly (Fulham), Paul McShane (Hull City), Darren O'Dea (Ipswich Town), 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), Keith Treacy (Preston North End), Robbie Keane (Tottenham Hotspur), Kevin Doyle (Wolves), Shane Long (Reading), Cillian Sheridan (CSKA Sofia).