The defender was injured during Saturday’s 2-1 win over Nottingham Forest and limped early in the second half.
The wood has undergone analysis and is due to undergo further evaluation and review with a consultant in the coming days, but there are fears he could be out for months.
The summer signing, who joined from Ajax for an initial fee of £34.2million, was mainly brought in to play at right-back but played on the left against Forest. It can also operate in the heart of defense.
His injury could also affect the left-back Kieran Tierney. The Scot has slipped down the pecking order at Arsenal and is a target for Newcastle.
The Magpies would ideally like to sign Tierney on loan, with a view to a permanent move, but Arsenal may be reluctant to let him go now.