It will rule the 27-year-old out of the Eagles' Marsh Community Series clash against Essendon on February 27.
Darling will also be unavailable for selection in the State of Origin Bushfire Relief match (February 28), with doubt around his place in the Eagles' second pre-season hitout with Fremantle (March 7).
"It was friendly fire in training and unfortunately he has a small fracture of the cheekbone," Eagles head of football Craig Vozzo told westcoasteagles.com.au.
"He will build back into training, just avoiding contact for the next few weeks, but we're still confident in terms of round one."
The Eagles also indicated All-Australian backman Jeremy McGovern (heel) would increase his training loads with the main group next week.
Fellow defender Tom Barrass, who has been dealing with a foot complaint, is expected to re-join the main group in coming weeks.
Doubt remains over McGovern and Barrass lining up in either of the pre-season matches.
Brendon Ah Chee (iliotibial band), Josh Rotham (hamstring), Nathan Vardy (ankle), Tom Hickey (calf) and Oscar Allen (hernia) are also nearing full fitness.
"Nathan, Tommy and Oscar are in the same boat in modified training building into full training, and you'll see more and more of them on the track in main training over the next few weeks," Vozzo said.
Midfielder Luke Foley will resume full training in coming weeks after stepping aside following a stress injury in his pubic bone.