Moody limped out of Saturday's 23-19 win against Wales with a recurrence of the knee ligament problem that kept him sidelined for England's RBS 6 Nations title campaign.
The England captain has had his left knee scanned and the results were on Monday being studied by the team's medics, with a conclusion expected on Tuesday.
Johnson said: "The bad news would be that he has got an eight week injury that would put him out of the World Cup. I don't think it is going to put him out of the tournament, but we'll see.
"It is not great that he has got an injury, but I don't think it is on the very bad side of knee injuries."
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