Cancelo swapped Valencia for San Siro last week, moving on a season-long loan deal, with Inter holding the option to make the move permanent.
While training with Fernando Santos' European champions ahead of their World Cup qualifiers with Faroe Islands and Hungary the full-back tore ligaments in his knee and faces time out recovering from the injury.
"Joao Cancelo underwent medical tests this afternoon in Rozzano after picking up an injury while training with Portugal," an Inter statement read.
"The tests revealed that he has suffered a tear to the medial collateral ligament in his right knee.
"Cancelo's condition will be evaluated week to week."