The 38-year-old Brazilian is having scans on his left knee and Chelsea are worried that he may have damaged his medial collateral ligament.
Silva has been in brilliant form this season and losing him would be a major blow for the Blues, who are 14 points off the top four in the Premier League.
Chelsea trail Dortmund 1-0 from the first leg and failure to go through in the Champions League would add to the pressure on Potter.
Chelsea’s owners continue to back Potter for now but their next two games – at home to Leeds and Dortmund – could be crucial to his future.
Silva faces being out until after the March international break and could miss up to six matches.
Potter has plenty of other options in Kalidou Koulibaly, Wesley Fofana, Benoit Badiashile - who is unregistered in Europe - and Trevoh Chalobah, but Silva will be hard to replace in the Chelsea defence.
He has played 2,287 minutes this season, more than any other Chelsea player, and is one of the few to come out of a difficult period with any credit. His form has been so good he was recently rewarded with a new contract that will keep him at Stamford Bridge beyond his 39th birthday.
Chelsea, meanwhile, hope to be boosted by the return of both N’Golo Kante and Christian Pulisic, who are expected to step up their recovery from long-term injuries this week.
They continue to monitor Cesar Azpilicueta following his head injury against Southampton.