The 23-year-old sustained the season-ending injury in the Gunners 2-2 draw with Manchester United.
But the former Bolton man, who recently cemented his place at the heart of Unai Emery's defence, is remaining positive for his recovery.
He took to Instagram to post to his 400k followers that the surgery was successful.
He wrote: "Happy that the surgery went well. Road to recovery starts now."
Holding's injury blow is just one of a series of sidelined players that the Emirates chief is dealing with.
The Gunners medical staff were handed another patient yesterday after Hector Bellerin was withdrawn in Arsenal's 3-2 defeat to Southampton.
Bellerin received treatment on the pitch just before half-time but did not make it out for the second-half.
Arsenal were forced to start full-back Stephan Lichtsteiner and Laurent Koscielny, who has played just three times this season, at centre-back.
Defensive midfielder Granit Xhaka was also used in defence for the Spaniard – who will now need to think seriously about recruiting a defender at the turn of the year.
In October, new club executive Raul Sanllehi said Arsenal will only dip into the transfer market in January in case of an emergency.
And with the queue for the medical room growing with every game – there is no doubting the Gunners are in an injury crisis.
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