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 took place from June 11th to July 19th in the United States, Canada and Mexico. The tournament featured 48 national teams and was won by Spain, who beat Argentina in the final.
Full schedule and results | Group standings and bracket | Past winners of the tournament | Our team of the tournament | About the 2030 World Cup