The forward had been in brilliant form for the Black Cats and headed into last week's Carabao Cup clash with Arsenal with five goals in as many matches. But he broke down during the tie.
Speaking to the media ahead of his side's trip to Doncaster on Monday, Johnson revealed his loan star would be out for at least three months - but he fears it could be longer.
He said: “It's a bad one for Nathan.
“I would say it will be a minimum of three months, but it could be the season."
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