The 25-year-old Arsenal forward is thought to have torn a ligament during the meeting in Houston and is reportedly facing up to six months out of action.
“We will see what the doctors say, but it is a pretty big tear and I will have to undergo an operation,” he said to reporters.
Campbell later added on his official website: “It’s sad and difficult to have to leave the national team, it’s tough when injuries like this stop you from competing and defending your country.
“I gave everything, as I always do. Now I have to think about recovering to come back stronger and to support my team-mates 100 per cent. The objective remains the same.”