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The Belgian star had to be replaced by Gabriel Jesus in the 60th minute on Saturday evening following a bodycheck by Rudiger.
The Chelsea defender was booked for the challenge on De Bruyne, who left the field in tears at the Estadio do Dragao.
De Bruyne posted on Twitter on Sunday morning: "Hi guys just got back from the hospital.
"My diagnosis is Acute nose bone fracture and left orbital fracture. I feel okay now. Still disappointed about yesterday obviously but we will be back."
Rudiger took to Twitter on Sunday afternoon to reveal he had been in touch with De Bruyne to wish him well.
The German posted: "I'm really sorry for DeBruyneKev's injury.
"Of course this was not intentional from me - I've already been in touch with Kevin personally and I really wish him a speedy recovery and hope we can see him back on the pitch very soon again."
Additional reporting by PA.