The Brazil international sustained the setback in the opening 15 minutes of the derby and he was subsequently replaced by Jakub Kiwior.
It was initially reported that he could be sidelined for weeks, but Arsenal have clarified that Magalhaes won't be involved for the rest of the campaign.
The club released a statement that the defender needs a surgery for the setback. The procedure will happen immediately such that he can recover in time for the start of the 2025/26 season.
The news is a huge blow for the Gunners, considering Kiwior has been unconvincing as a central defensive partner for William Saliba. He has been prone to plenty of defensive errors.
The Poland international faces a huge test of his credentials when the Gunners take on Real Madrid in the Champions League quarter-final ties.