Oxlade-Chamberlain fell awkwardly after a clumsy challenge by Carlos Gruezo in England's 2-2 draw against Ecuador at Sun Life Stadium in Miami on Wednesday night.
Scans taken on Thursday showed the Arsenal midfielder suffered medial ligament damage to the right knee.
It is understood Oxlade-Chamberlain only sprained the ligament and did not tear it. He is expected to be out for two to three weeks.
He is therefore unlikely to play a part in England's first two group matches, but that may not stop him from travelling to Brazil with the squad on Saturday night.
Speaking at a Vauxhall-sponsored England fans' forum, England manager Hodgson said: "We will do everything in our power to keep him (in the squad). Our medical team are optimistic and he is optimistic.
"We can't say how long for certain it will take him to recover but obviously he will get very extensive treatment.
"We have the right to replace him if we want to up to 24 hours before the first game.
"We will do everything we can to keep him with us because: a) we would we like to think we might go beyond the group stage although we can't guarantee it, we are certainly planning for it.
"And b) he played so well yesterday. He was undoubtedly our best player in the time he played and it would be a major blow if we lose him. "
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