The 25-year-old picked up the complaint during the club's pre-season tour of America earlier this summer.
"We're just managing a slight problem with his knee at this moment in time," said Norwich manager Chris Hughton.
"He is another one who did the first part of pre-season and he did very well. Of course when it came round to these most recent period of games we have not been able to use him but we are hopeful that he is going to be training next week and to push on from there."
The problem has also forced Pilkington to withdraw from the Republic of Ireland squad for next Wednesday's friendly against Wales.