The 23-year-old suffered the knee injury during the first half of Wednesday's 2-2 draw with Manchester United at Old Trafford, which left Unai Emery's side fifth in the table.
"Further to the injury sustained during our match at Manchester United on Wednesday night, we can confirm that Rob Holding has ruptured the anterior cruciate ligament of his left knee," said a statement on arsenal.com.
"Rob will undergo surgery to repair this in the coming days. The rehabilitation process is expected to take between six to nine months.
"Everyone at the club will now be working as hard as we can to ensure Rob is back on the pitch as soon as possible."
Holding began his career with Bolton before joining Arsenal as a 20-year-old in 2016. He has been a consistent member of the Gunners' back four under Emery this season, starting 15 games.
The defender wrote on Twitter: "Just want to say a big thank you to all the fans, players and staff members for the support during the past couple of days. Gutted to get injured during a strong period for the team."
Emery tweeted: "We're having a good week even if it's being tough because of the injuries -you'll get well soon and stronger Rob!-, but now let's keep going forward and focused on @htafcdotcom to make it a great week end. Together we are stronger... @Arsenal !"