The youngster looked to be on course to be selected for England’s World Cup squad for June’s world showpiece in Brazil.
He is expected to be ready for action again in October after picking up the injury against Manchester City on Saturday.
“Everything will be done to deliver a speedy recovery,” said Southampton director Les Reed.
“Jay is naturally disappointed, but is determined to get back playing for Saints as soon as possible.
“He has asked us to pass on his gratitude to everybody who has shown him their concern and sympathy during the 48 or so hours since his injury.”