The 37-year-old striker had an operation on his meniscus at a clinic in Madrid on Thursday after experiencing discomfort during Deportivo's 1-1 draw with Real Betis on Sunday.
Deportivo confirmed that Aubameyang will now return to La Coruna to begin his recovery.
"His progress will determine when he returns to training," the club said in a statement.
The injury is a significant blow for Deportivo, with Aubameyang having played a major role in their strong return to La Liga following promotion.
The Gabon international has scored five of Deportivo's 10 league goals this season, helping them collect 10 points from their opening seven matches and move into seventh place.
Aubameyang, Gabon's all-time leading scorer, recently stepped away from international football after claiming he felt "humiliated" when the Gabonese government singled him out over the country's disappointing 2025 Africa Cup of Nations campaign.
His immediate focus will now be on recovering from the knee operation and returning to action with Deportivo.
Deportivo's next La Liga match is against Real Sociedad at Anoeta on Sunday, October 11.
