The star midfielder was nearing a return from the syndesmosis injury suffered in April, but he relapsed during weekend training.
Griffen will sit out the next three months, meaning he could make a return for finals in September.
“It’s a more severe injury this time around and required surgery, which he underwent on Monday,” Giants performance boss David Joyce told the club’s website.
“Unfortunately during a drill at training, he’s re-injured the ligaments at the top of his ankle.”
Griffen has not played since round three.
The ladder-leading Giants are also without stars Brett Deledio, Devon Smith and Stephen Coniglio due to injuries.
But forwards Steve Johnson (knee) and Rory Lobb (groin) are a chance return against Carlton at Etihad Stadium on Sunday, pending fitness tests.
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