Giants teammate Sam Taylor will also spend time out of action with a concussion, but he is expected to return for their opening-round clash against Collingwood.
Green picked up the calf complaint during an intra-club match simulation four weeks out from the season, the Giants confirmed on Tuesday.
GWS are hoping Green will only miss their matches against the Magpies and Melbourne before a round-two bye.
At worst, the 24-year-old will spend six weeks on the sidelines.
Green joins forward Callum Brown (hamstring) and midfielder Ryan Angwin (ankle) on the injury list, the duo also facing four to six weeks in rehabilitation.
Taylor suffered a heavy knock during the same simulation after a marking contest with teammates Jesse Hogan and Aaron Cadman.Â
He will miss their match simulation against Sydney on Friday, but could return for their final pre-season hit-out against Carlton the following week.
The Giants are hopeful veteran midfielder Stephen Coniglio will line up for opening round.
Ruled out for their Swans clash, Coniglio is likely to feature against Carlton after undergoing facial surgery and a shoulder reconstruction in the off-season.
Coniglio had copped a heavy blow to his cheekbone in a marking contest in the Giants' semi-final loss to eventual premiers Brisbane.
Defender Josh Fahey - who must first serve a four-match suspension - remains on the sidelines indefinitely with a foot injury.
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