The 33-year-old will miss the T20 World Cup in Australia and his country's Test series in Pakistan.
Bairstow revealed he let out "uncontrollable screams" after sustaining the injury early last month having slipped during a round of golf.
"The actual injury was as such… a broken fibula in three places which required a plate, I dislocated my ankle which in turn meant I did my syndesmosis joint and lateral ligament along with a couple more bits," he posted on Instagram. "All in all I have done a proper job on it!
"Anyway… on the positive side the operation went well and I am now three weeks post surgery and my staples have been removed. It's now all about swelling prevention and getting my ankle moving once again. These next few weeks/couple of months are the key to the recovery.
"As for a time scale on return to play I'm afraid it is too early to say, the first targets in mind are getting me back on my two feet again and making sure its right.
"One thing is for sure and that is I shall not be partaking in anything more during 2022…however I cannot wait for what 2023 holds!!"
Prior to the freak injury, Bairstow had been in fine form for his country and was later named 2022 LV= Insurance Test Player of the Summer.
The Yorkshireman hit four hundreds and amassed 681 runs at an average of 75.6 during the best year of his Test career.
Speaking about the injury he sustained after playing the third hole at Pannal Golf Club near Harrogate, he told the Telegraph: "Normally when you slip you fall on your bum, which would have been fine as there's plenty of cushion in there.
"Except this time I tried to regain my balance, my left ankle turned right, dislocated and my weight went through my left lower leg. I heard it snap straight away.
"I took a couple of steps down then slipped. By the time I crumpled into a heap, I was three-quarters of the way down. It's all a blur, it happened so quickly.
"I yelped. Uncontrollable screams, the sort you hear on a rugby field. The adrenaline kicked in, and I knew I needed an ambulance. The next three hours without painkillers were not too fun."