McGlynn collided heavily with Freo ruckman Zac Clarke in the third quarter and was not able to return to the field. He had been a powerful force for the Swans up until that point, amassing 17 disposals and kicking three goals.
McGlynn was taken to Perth's Sir Charles Gairdner Hospital after the game where scans showed a triple fracture of the cheekbone.
He had surgery early on Sunday morning and will remain in Perth for several days.
Swans doctor Nathan Gibbs said the injury may mean McGlynn does not play again this year depending on how deep his team progresses in the finals series.
"At this stage we expect Ben will miss at least three weeks of football, but we will re-assess his condition after the surgery,'' Gibbs said.
"Our main concern at this time is for Ben's welfare, and we do expect him to make a full recovery.''
