The 71-year-old actor, who is filming the seventh film in the franchise, was at Pinewood Studios when the door fell on him.
He reportedly fell to the floor in agony and after being assessed on set by medics was taken to John Radcliffe hospital in Oxford.
The British hospital has a trauma unit that specialises in fracture clinics, and provides facilities for radiological investigation and therapy treatment for all trauma patients.
It is thought Harrison has a fractured ankle and no major chest injuries but is awaiting further tests.
In a statement, Disney said: "Harrison Ford sustained an ankle injury during filming today on the set of Star Wars: Episode VII. He was taken to a local hospital and is receiving care. Shooting will continue as planned while recuperates."
The set is now being checked to ensure it meets all safety regulations but the Health And Safety Executive has launched an investigation into the incident.
Lupita Nyong'o and Gwendoline Christie join Harrison Ford in Star Wars
Joining Harrison in the Star Wars film, the first since 2005, are his original co-stars Carrie Fisher and Mark Hamill. The trio became household names after the first Star Wars movie in 1977.
Other actors joining the original three include Girls star Adam Driver, Inside Llewyn Davis actor Oscar Isaac, Domnhall Gleeson, and British actor John Boyega. Andy Serkis, Max von Sydow, and Daisy Ridley will also star.
Earlier in June Lupita Nyong'o and Gwendoline Christie were also confirmed to also have a starring role.