White, 28, was forced off and replaced by Myles Lewis-Skelly in the 31st minute of their home game against bottom placed Wolves.
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The right-back only recently returned to fitness having suffered various injury issues over the past couple of seasons.
Arsenal have been hit with injuries to several key players since the start of the season, particularly in defence with William Saliba, Gabriel, and Cristhian Mosquera, among others all sidelined at one point or another.
Mikel Arteta has faced heavy criticism for his training methods and use of players who are not quite 100% as Arsenal head into the hectic festive period.