Lars Bender, who plays for Bayer Leverkusen, suffered a muscle tear in his right thigh during his side's 1-1 draw with Bayern Munich on Saturday.
The 30-year-old Westermann has played 26 games for Germany. His last appearance was in a friendly against the United States on June 2.
Germany would secure qualification for next year's World Cup in Brazil with a win against Ireland in Cologne on Friday, while even a draw virtually assures progress before the game against second-place Sweden in Stockholm four days later.
Germany leads group C by five points and enjoys a comfortably superior goal difference ahead of the final two games.