The injury, to his left knee, was sustained during the second quarter of Saturday night's seven-point win over Carlton.
It now leaves the Lions without their first two choices in the ruck, with No.1 option Matthew Leuenberger still another eight weeks from returning following a meniscus tear.
West, 26, was recruited from Geelong in the off-season, and is the second Lion to do an ACL this season after Daniel Rich injured his right kneein round three.
Coach Justin Leppitsch said Stefan Martin, who has played two reserves games following a long layoff, was the logical choice to replace West.
However, he also kept the door open for the elevation of basketball convert Archie Smith.
"I love the way Archie plays," Leppitsch said following Saturday night's win.
"At this point in time, unless things change, he's (Martin) the logical choice, but in my heart, I would like to see another one (debutant) go around."
West and the club will now determine the best course of action for his rehabilitation.
Twitter: @AFL_mikewhiting
