The 30-year-old has been managing the problem since March and was forced to undergo surgery, although she recovered in time to represent England at this summer's World Cup.
Since the resumption of domestic football, Bright has continued to feature regularly in the heart of the Blues' backline, starting each of their first six Women's Super League fixtures and their opening Champions League group-stage clash with Real Madrid on November 15.
However, the defender was then absent for the 5-1 thrashing of Liverpool last weekend, before also being forced to sit out the Blues' 4-1 Champions League success over Paris FC on Thursday night.
Speaking to the media ahead of the continental clash, Chelsea boss Emma Hayes admitted that Bright's load needed to be carefully managed, as she had rushed herself back to be ready for the World Cup.
"Having so many games in quick succession, we are managing her load. We wanted to give her a little bit of extra time, but she is very much in doubt for tomorrow," Hayes told the media.
"Prior to the World Cup, she had surgery on her knee, so her preparation going into the World Cup wasn't ideal. She rushed herself back from the World Cup and into the Chelsea season. Perhaps she needed a little bit longer.
"Her knee is a little big angry at the minute. It's nothing too detrimental, but we are listening to her body and how she is feeling. We are taking it on a day-to-day basis."
Hayes's comments poured doubt on Bright's availability for the Nations League, and England have now confirmed that the 30-year-old has pulled out of the squad for their final two group matches.
While Bright continues her treatment at Chelsea, Wiegman has replaced her with uncapped Manchester United defender Millie Turner, who previously played for the Lionesses at Under-19s and Under-23s level.
The 27-year-old earned her first senior call-up to the England squad during Phil Neville's reign, joining 29 other players as part of a training camp in September 2020, and she has contributed one goal in nine matches for Man United this season.
England have won two and lost two of their opening four matches in the inaugural Women's Nations League and sit in third place in League A Group 1, which would put the European champions at risk of demotion to the second tier via the promotion/relegation playoffs.
Wiegman's team sit one point behind Belgium and three point below the Netherlands, whom they will take on at Wembley on December 1, four days before a clash with basement side Scotland at Hampden Park.