Can shared a picture of his teammate on Instagram alongside the caption: “Get well soon bro! I believe in you that you will come back stronger.”
Germany revealed that Rudiger has been ruled out of Euro 2016 after tearing cruciate knee ligaments in training.
The 23-year-old was included in the 23-man squad and preparing for the European Championships when he suffered the injury.
“A decision on a new player has yet to be taken,” said a Germany statement.
Germany will now be without Rudiger and centre-backs may not have Mats Hummels available either who has not fully recovered from a leg muscle injury.
The German side will take on Northern Ireland, Poland and Ukraine in their Euro 2016 group.
Can has been called up to the Germany side but will be deployed in defence instead of central midfield as he does for Liverpool.
The Liverpool star is one of two Germany intentional players of Turkish origin in the side – the other being Arsenal playmaker Mesut Ozil.