The defender suffered a tear to the ligament in his right ankle on Sunday and faces a race to be fit for the return leg.
Hummels, who suffered a tear to the ligament in his right ankle on Sunday and faces a race to be fit for the return leg in Madrid on April 18, told the German daily Bild: "I definitely won't be on the pitch on Wednesday."
"Very sad about missing at least the next two games," the towering centre-back added on Twitter and posted a picture of him wearing a special recovery boot on Instagram under the caption, "Already trying to recover as fast as possible".
As well as this week's Champions League first leg, Hummels will sit out Saturday's Bundesliga away match at Bayer Leverkusen at the very least.
With Hummels sidelined Jerome Boateng and Javi Martinez will resume their centre-back partnership having played in Saturday's 4-1 win over Borussia Dortmund.
Bayern are also waiting to see if Germany goalkeeper Manuel Neuer is fit as he is yet to resume training after a minor foot operation.
There was some good news for Bayern head coach Carlo Ancelotti as Germany forward Thomas Mueller returned to training on Sunday and is expected to be fit to face Real after an ankle injury.
Madrid will be without Pepe after the Portugal centre-back broke two ribs in the 1-1 draw with Atletico Madrid on Saturday and French defender Raphael Varane will also miss Wednesday's game.