Wellingham damaged ankle ligaments when he landed awkwardly bouncing on a trampoline and will wear a moon boot for the next couple of weeks.
Fantasy face-off: Nic Nat v Jacobs
The former Collingwood midfielder won't require surgery, but he will miss the rest of West Coast's pre-season matches, putting him in doubt for the round one derby on March 23.
Wellingham was impressive in West Coast's NAB Cup win over Fremantle on Saturday night, finishing with eight disposals and two clearances in the shortened match.
"[It was a] short hit-out for him, but he showed why we picked him," coach John Worsfold said post-match.
"We know why we've got him here and what role he's going to play and he did it well."
West Coast will have this weekend off before playing Collingwood on March 3.
Ruckman Dean Cox has declared himself available for that clash, with Matt Rosa, Beau Waters, Josh Kennedy, Sam Butler and Brad Sheppard also pushing for inclusion.
Nathan Schmook is a reporter for AFL Media. Follow him on Twitter: @AFL_Nathan