The centre-back has been unable to take part in squad training at Germany's preparation camp in Ancona, and even though he remains confident he will be recovered in time to feature at the finals in France, he could miss the world champions' first game of the tournament.
"The injury is healing, but it will be a while," Hummels told FAZ.
"I will not resume squad training during the training camp in Ancona.
"When I'll be back? It depends on how I feel and what the coach thinks about my fitness. Ideally I'd be ready for the first game against Ukraine, but it would not be a problem if I make my comeback in the second or third game.
"The most important thing is that I will be at 100 per cent. I cannot help the team otherwise.
"You can never really predict what will happen, but I will play a role at the Euros if everything goes according to plan."