The Germany international has an abdominal strain which coach Thorsten Fink says he is unwilling to take any chances with heading into Saturday's game against Monchengladbach
Coach Thorsten Fink says that, although the injury is only minor, he is not willing to play Adler at the weekend and risk losing him for a longer period of time.
"René has fallen to 90% from 95%," Fink told Bild. "He felt a sharp pain. We don't want to take any chances. It is an abdominal muscle strain, but it is not torn yet
"If that happens we lose Rene for three or four weeks. It is a risk we do not want to take."
Following Hamburg's terrific 4-1 win at Dortmund last weekend, Adler's injury has got progressively worse, and he missed training on both Tuesday and Wednesday.
Jaroslav Drobny will replace Adler in the side on Saturday for what will be his first league appearance of the season.
And although Adler has been the obvious first-choice this season, Fink has plenty of faith in 33-year-old Drobny.
He added: "I have the greatest confidence in Drobny. He will do the right things when called upon."
Hamburg lie in seventh place in the Bundesliga table, just one point and one place clear of Monchengladbach, ahead of Saturday's showdown.