The experienced midfielder was injured after falling over advertising boards while celebrating the last-16 win at the Estadio Azteca.
Henderson was taken from the pitch on a stretcher before being transported to hospital for treatment.
The injury has ended the 36-year-old Brentford midfielder's World Cup campaign, although he is expected to remain with the England squad at their base in Kansas City as they continue their tournament.
Henderson shared an update with supporters on Instagram after the operation.
"Surgery done. Let's get ready for the big one on Saturday.
"Thank you to all the staff that looked after me at Kansas City Orthopaedic Institute, especially the three surgeons who carried out the operation."
England will now prepare for a tough quarter-final against Erling Haaland's Norway in Miami on Saturday.
