Bright skippered the England women's team at last summer's World Cup, where they lost to Spain in the final. The defender recovered from a knee injury to captain the Lionesses in the absence of Leah Williamson, but the knee is still proving troublesome.
With Bright sidelined, Manchester United's Millie Turner has been called up. Turner has featured previously for England's under-19 and U23 squads and will look to make her international debut in England's final two matches of the year.
England need to defeat Netherlands and Scotland to stand a chance of topping their Nations League group. England are the designated team for Team GB's qualification for the Olympics, and need to reach the Nations League final to secure a spot at Paris 2024.
Bright missed Chelsea's key Champions League group match against Paris FC on Thursday at Stamford Bridge with Emma Hayes describing Bright's injury as "little bit angry."
England face the Netherlands on Dec.1 at Wembley and then travel to Scotland on Dec. 5.