Japanese right-back Tomiyasu came off nine minutes into Arsenal's Europa League round-of-16 encounter with Portuguese side Sporting CP after he slipped awkwardly during a challenge and hurt his knee.
Arteta had said at the time that they were immediately concerned as the 24-year-old Japan international is "not one to exaggerate things."
"Following his substitution during last Thursday's Europa League match, subsequent assessments have confirmed that Takehiro Tomiyasu sustained a significant injury to his right knee," Arsenal said in a statement.
"Tomi has had successful surgery in London on Tuesday and will be ruled out for the remainder of this season."
Arsenal were knocked out of the Europa League in a penalty shootout but they are still top of the Premier League with an eight-point lead over Manchester City, who have a game in hand.