The Brentford player fell over advertising hoardings during celebrations after the 3-2 victory at the Estadio Azteca, which took them through to the quarter-finals.
The 36-year-old was taken to hospital, having left the field on a stretcher.
He is now set to miss the remainder of the World Cup but is expected to stay with the team at their Kansas City base.
"Surgery done. Let's get ready for the big one on Saturday," Henderson posted on Instagram.
"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 face Erling Haaland's Norway in the last eight of the World Cup in Miami on Saturday.
FIFA World Cup 2026
The 2026 World Cup is taking place from June 11th to July 19th in the United States, Canada and Mexico. The tournament features 48 national teams and is played at 16 modern stadiums.
Match schedule and times | Group standings and knockout bracket | How to watch the World Cup | World Cup Format | Past winners of the tournament