Brady has not recovered fully from a hernia operation and Clark has a foot tendon problem.
No additional players have been called into the squad by new boss Martin O'Neill.
Ireland face Latvia in Dublin on November 15, before heading to Poznan to take on Poland the following Tuesday.
Goalkeepers: David Forde (Millwall), Keiren Westwood (Sunderland), Rob Elliot (Newcastle United).
Defenders: Sean St Ledger (Leicester City), Marc Wilson (Stoke City), Seamus Coleman (Everton), John O'Shea (Sunderland), Alex Pearce (Reading), Stephen Kelly (Reading), Joey O'Brien (West Ham).
Midfielders: James McCarthy (Everton), Stephen Ward (Brighton), Glenn Whelan (Stoke City), Paul Green (Leeds United), Andy Reid (Nottingham Forest), Aiden McGeady (Spartak Moscow), Anthony Pilkington (Norwich City), James McClean (Wigan Athletic), Stephen Quinn (Hull City), Wes Hoolahan (Norwich City).
Forwards: Shane Long (West Brom), Robbie Keane (LA Galaxy), Jonathan Walters (Stoke City), Kevin Doyle (Wolves), Anthony Stokes (Celtic).