The duo will be replaced by Leeds United forward Paul Green and West Ham goalkeeper Stephen Henderson, who is currently on loan at Bournemouth.
Walters had been struggling with a groin injury prior to Stoke's 1-0 defeat at Fulham on Saturday but managed to play 84 minutes at Craven Cottage before being replaced by Peter Crouch.
The nature of Westwood's injury has not been confirmed ahead of Ireland Group C double header which begins with a difficult fixture against Germany in Cologne on Friday.
Meanwhile, Boruussia Dortmund manager Jurgen Klopp has cast doubt over Sven Bender's participation in for Germany's World Cup qualification double-header.
Germany currently occupy top spot in Group C and need just a point from their remaining two group matches to qualify for next year's World Cup in Brazil.
But Joachim Loew may have to make do without Bender for the matches against Ireland and Sweden after Klopp gave an update on the defensive midfielder's fitness following his substitution during Saturday's 2-0 defeat at Borussia Moenchengladbach.
"Sven is black and blue, I must telephone Joachim Loew and see what he wants to do, then we'll see what happens after that," said the Dortmund manager.
Bender's team-mate Mads Hummels faces an anxious wait to see whether he returns to Loew's starting line-up for Friday's match against Ireland after another below-par performance against Monchengladbach where the 24-year-old conceded a penalty.