The France international may also be in danger of missing Euro 2024, which starts in just over a month, after Real Madrid revealed he has "a stress fracture in his left foot" without offering any timetable for his return.
Real qualified for the final after overcoming Bayern Munich 4-3 on aggregate on Wednesday. The 24-year-old suffered a similar injury in October 23 which kept him out of action for six weeks.
Tchouameni was substituted in Wednesday's second leg in Madrid with 20 minutes remaining.
France manager Didier Deschamps will announce a list of 23 or 26 players live on France's TF1 evening news on May 16.
France travel to Germany as co-favourites with England and open their campaign on June 17 against Austria praying that their key defensive midfielder will be on the pitch in Dusseldorf.