Holding, who has nailed down a regular place in Unai Emery’s team this season, was forced off in the 2-2 draw against Manchester United on Wednesday.
Emery revealed in his post-match press conference that he feared the 23-year-old had suffered a “big injury”.
A statement released by Arsenal on Thursday read: “Left knee. Returned to London during match on Wednesday night.
“Will have further tests and assessments over the next 48 hours.
“Further updates will be communicated in due course.”
Holding has made 16 appearances in all competitions since winning a spot in the starting XI towards the end of September.
Emery has been using a three-at-the-back formation in recent weeks but the injury blow is likely to see the Arsenal boss revert to a four-man defence.
Holding lasted 36 minutes at Old Trafford before a collision with Marcus Rashford forced him off.
Speaking after the final whistle, Emery said: “The worst news is the Rob Holding injury.
“The doctors think maybe it is a big injury but we are going to wait (to find out), it is his knee.”
There is a glimmer of hope on the horizon for Emery, who is hoping to have veteran centre-back Laurent Koscielny available from next week.
The Frenchman is yet to play a competitive match under Arsene Wenger’s successor, having ruptured his Achilles tendon last season.