Japanese right back Tomiyasu came off nine minutes into Arsenal's Europa League last-16 encounter with Portuguese side Sporting after he slipped awkwardly during a challenge and hurt his knee.
Arteta had said at the time that they were immediately concerned as the 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.
The north London club also lost defender William Saliba (21) to a back injury in the same game, with France opting to replace him in their squad for the upcoming Euro 2024 qualifiers.