Oubina, who Blues have borrowed for the season from Celta Vigo, suffered the injury in Saturday's 0-0 Premier League draw with Liverpool at Anfield.
The 25-year-old underwent medical tests over the weekend which confirmed the damage to his left knee.
"This is terrible because I arrived in the Premier League with much anticipation, " Oubina told the Spanish media.
"I wanted to demonstrate that I would be able to play in this competition. From the first moment I felt the injury, I feared the worst."
Oubina, who has two caps for Spain, suffered a similar injury to his right knee in 1997.
