The 26-year-old, who is regarded as one of the best stoppers in La Liga, is believed to be suffering from tendinitis in his right shoulder.
"I did the tests on the shoulder and it was seen that I have an injury. It is not a serious injury but I have to take care. Shoulders for a goalkeeper are very delicate parts for the type of work that we have to do," he told reporters at a press conference.
"I feel a lot of pain, it hurts me to make certain movements. The doctor has told me it is something I have to be careful with because if I do not, I can cause a more serious injury that will hurt me enough not to play.
"I hope to have recovered in time for the League resuming, but I am aware that I will not risk anything. I want to be 100% and I'll wait until I am without pain."
Navas, who has won 50 caps for Costa Rica, has been unable to join up with his national team this week due to the issue.