The injury forced Oscar to miss the first leg clash with Atletico and the win at Liverpool last weekend, and he was an unused subsititute in the 3-1 defeat to Atletico after failing to shake off his hip problem.
The 22-year-old admits he is likely to miss the final two games of Chelsea's Premier League campaign as he does not want to aggravate the injury ahead of the World Cup with Brazil next month.
"I'm not playing because I felt a pain due to an injury to my hip, so, in the last game against Liverpool, I was not called on," Oscar told Globo Sport.
"I warmed up [against Atletico], but Mourinho knew that I could hardly play.
"Maybe I will not play the next game (against Norwich) because I could suffer a more serious injury to my hip and he knows it.
"We're aiming to try and play me in the final clash of the Premier League (Cardiff) but I have to take care for the World Cup.
"We still have two very important games in the Premier League because Chelsea can still be champions, but it is important I rest because the World Cup is here."