Real were not expected to struggle in Group G as they look to continue their recent dominance of the Champions League, but Julen Lopetegui's side went behind inside two minutes in Moscow following a mistake by Toni Kroos.
Madrid had 26 shots but home keeper Igor Akinfeev had only three saves to make, with centre-forward Benzema now six games without a goal.
They began well with Hummels given space in the box to head home an excellent Arjen Robben cross.
The last week has also seen Madrid beaten 3-0 at Sevilla and drawing 0-0 at home to neighbours Atletico Madrid in La Liga, but Lopetegui maintained that he was sure they would return to form soon.
Nevertheless, the hosts held on to move to the top of Group G above Real, who dropped down to second. If Bale is unable to play, Karim Benzema will play a bigger role against CSKA while Marco Asensio and Lucas Vazquez will start on the wing.
Lopetegui's side will have a chance to end their mini-crisis when they travel to Deportivo Alaves on Saturday.
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Al Manchester United le costó mucho establecer buenas secuencias de pase, y apenas desordenaba a su rival, que logró el 2-0 en el minuto 43, cuando Lindelöf marcó en propia portería.
Navas said: "We are sad because they had one chance and took it".
DF Nacho, 6 - Real Madrid, in general, were shaky whenever Moscow broke through. Real Madrid hit the crossbar in the first half through Casemiro, but, despite plenty of second-half pressure, the visitors, now winless in three games, could not find a way back into the match. "We need to have options for every moment of the game, but without compromising our outlook and playing style".
Madrid have three games before facing Barcelona at the Camp Nou on October 28, a match that is shaping up to be a battle of the beleaguered, although much could change before then.
The absence of the established names meant a youthful line-up, which included a debut for 21-year-old left-back Sergio Reguilon, who joined the club's academy aged eight.
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Dybala scored in the fifth, 33rd and 69th minutes against Young Boys.
Brazilian Junior Moraes had struck either side of half-time to seemingly put the Ukranians in control.
Dani Ceballos also started while summer signing Alvaro Odriozola came on for his Champions League debut after Dani Carvajal pulled up injured.