Westwood, who has played eight times for the Owls this season, has been overlooked on this occasion, with Ireland boss Mick McCarthy selecting Darren Randolph, Mark Travers and Kieran O’Hara as his three shot-stoppers.
Westwood, 34, was selected in the Republic squad last month but pulled out with a knee injury.
McCarthy has included Blackburn Rovers duo Darragh Lenihan and Greg Cunningham in his 24-man squad.
"Terry Connor has been to watch Darragh and Greg play for Blackburn and they have shown him they will be good additions for this squad," said McCarthy.
"Enda Stevens is suspended for the game in Tbilisi against Georgia and Greg is one of the most experienced left-backs available to us. He was with us in the summer and he knows what we want.
"We’ve watched Darragh a number of times and Terry and the other scouts like his footballing ability. He has been in and around the squad before so I look forward to working with him."
The Republic sit top of Group D after five matches. They travel to Georgia on Saturday, October 12, before heading to Switzerland three days later.
Republic of Ireland Squad:
Goalkeepers: Darren Randolph (Middlesbrough), Mark Travers (AFC Bournemouth), Kieran O’Hara (Burton Albion, on loan from Manchester United)
Defenders: Seamus Coleman (Everton), Matt Doherty (Wolverhampton Wanderers), Kevin Long (Burnley), John Egan (Sheffield United), Darragh Lenihan (Blackburn Rovers), Greg Cunningham (Blackburn Rovers), Enda Stevens (Sheffield United)
Midfielders: Alan Browne (Preston North End), Josh Cullen (Charlton Athletic, on loan from West Ham United), Glenn Whelan (Heart of Midlothian), Conor Hourihane (Aston Villa), James McClean (Stoke City), Ronan Curtis (Portsmouth), Jeff Hendrick (Burnley), Callum O’Dowda (Bristol City), Jack Byrne (Shamrock Rovers)
Forwards: James Collins (Luton Town), Sean Maguire (Preston North End), Callum Robinson (Sheffield United), Alan Judge (Ipswich Town), Scott Hogan (Stoke City, on loan from Aston Villa)