Schweinsteiger suffered a partial ligament tear in his right knee at training on Tuesday ahead of friendlies with England and Italy.
The Manchester United midfielder hurt the same knee earlier in the season, with Hummels hopeful his compatriot can recover in time for the June 10 - July 10 continental showpiece in France.
"Of course, we all feel for Bastian after what happened," Hummels told the official German Football Association website.
"Everybody who has recurring injury problems knows how frustrating this can be.
"It is very annoying for Bastian, but also for the team. He is our captain. I obviously hope his injury will not keep him out of the Euros.
"We know that Bastian, like any other player, will be focused on getting back as soon as possible. The first day is all about frustration when you get injured, but from there on, you are entirely focused on making your comeback as soon as possible."