The US golfer sustained the injury while practicing at home, and although he has not put a timescale on his recovery, appears set to be absent from the season's opening major at Augusta next month.
In a statement posted on social media, Woods said: "As I began to ramp up my own training and practice at home, I felt a sharp pain in my left Achilles, which was deemed to be ruptured.
"This morning, Dr. Charlton Stucken of Hospital for Special Surgery in West Palm Beach, Florida performed a minimally-invasive Achilles tendon repair for a ruptured tendon.
"I am back home now and plan to focus on my recovery and rehab, thank you for all the support."
Dr. Stucken added in the statement: "The surgery went smoothly, and we expect a full recovery."
Woods hasn't competed in a PGA Tour event since The Open last July and has only played a limited schedule since suffering career-threatening injuries in a 2021 car crash.
The 15-time major winner has also been mourning the death of his mother Kultida and revealed last week that he has had little interest in practicing since her passing.
Speaking after he competed at his TGL event, the former world number one said: "This is the third time I've touched a club since my mom passed, so I haven't really gotten into it.
"My heart is really not into practicing right now. I've had so many other things to do with the Tour and trying to do other things.
"Once I start probably feeling a little bit better and start getting into it, I'll start looking at the schedule."