"We will see what the doctors say, but it is a pretty big tear and I will have to undergo an operation," the 25-year-old told reporters.
Campbell is out of the Gold Cup, a major blow to Costa Rica's chances of winning CONCACAF's regional title, but the injury also leaves his future at club level in doubt.
The winger's contract with Arsenal expires next summer, though he has spent most of his time with the Gunners on loan to various European clubs, with the injury potentially limiting chances of another loan this season.
"Leaving the national team is sad and hard to do. It is complicated when you get injured like this, it keeps you out of competitions and from representing your country. I gave it everything, as I always do. Now I have to think about my recovery to come back stronger than ever,"Campbell said on his personal website.
"I have to keep my head up and think about what's to come in the hands of God, my family and all those around me."