"Very bad news regarding AC. Torn ligaments in ankle. Operation tomorrow with top surgeon in USA. Will be playing in four months," Jack Sullivan, son of the club's co-owner David, tweeted in a question and answer session with his father on Thursday.
England striker Carroll also said on his Twitter account: "Going under the knife tomorrow morning and absolutely devastated to be missing the start of the season".
The 25-year-old was hurt on the tour of New Zealand but the club only discovered the full extent of the problem on Thursday.
Carroll's career has been blighted by injury since his permanent move from Liverpool last year.
He missed the majority of the 2013-14 season with a heel problem - managing just 15 Premier League appearances - and also failed to force his way into England's World Cup squad.
(Reporting by Tony Goodson, editing by Tony Jimenez)
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