The Italian suffered the fracture in victory at Manchester City on Saturday, playing an hour with a broken ankle.
"Sometimes football gives you its highs, and sometimes it challenges you in ways you don't expect," Vicario wrote on social media.
"I played 60 minutes at the Etihad with a broken bone in my ankle, giving absolutely everything I had for the team. Unfortunately there was no way around this one. I needed surgery.
"I'm disappointed I won't be able to help the team for a while."
Spurs haven't set a date for a playing return for the Italian.
- Get breaking football news faster with the new Tribal Football app! Download now on iOS and Android to stay ahead of all the latest transfers and football updates. Download now: App Store, Google Play