The 26-year-old was introduced as an 81st-minute substitute in the 2-0 UEFA Champions League defeat to Shakhtar Donetsk but appeared to twist his right knee as he chased down Fred in the final minute.
He had to be carried off the field, leaving the hosts, who had already made all three changes, with 10 men for the six minutes of time added on.
Manager Jagoba Arrasate expressed his concern over the injury after the match and his fears appear to have been confirmed, with Granero apparently having suffered an anterior cruciate ligament (ACL) injury.
A statement from the club read: "He (Granero) has suffered a twist in his right knee.
"Physical examination shows an anterior instability supports an ACL injury. Tomorrow (Wednesday) we will make additional tests to establish a definitive diagnosis."
His parent club Tweeted on Wednesday: "Best wishes for a speedy recovery to @eGranero11 following confirmation that he suffered an ACL injury last night".
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