The 78-year-old actor hurt his shoulder while rehearsing an action scene, reportedly involving a train, at Pinewood Studios in Buckinghamshire.
Director James Mangold will continue to shoot scenes without Ford while he recovers, but the crew are said to have been “warned there could be a four to five-week break”.
A source told The Sun that Ford “aggravated an old injury” and “requires surgery to put it right”.
In a statement, Disney said: “In the course of rehearsing for a fight scene, Harrison Ford sustained an injury involving his shoulder.
“Production will continue while the appropriate course of treatment is evaluated, and the filming schedule will be reconfigured as needed in the coming weeks.
This is not the first time Ford has sustained an injury during filming. His leg was broken by a hydraulic door in a freak accident on the set of the Millennium Falcon spaceship when he was playing Han Solo in the 2015 film Star Wars: The Force Awakens.
Ford has been filming the fifth Indiana Jones movie at several locations in the north of England and, earlier this month, North Shields residents had quite the shock when the star turned up at a popular local restaurant.
Ford will star in the new film opposite Phoebe Waller-Bridge and Mads Mikkelsen. He last played the character in 2008 film Indiana Jones and the Kingdom of the Crystal Skull.
The film is currently set to be released in July 2022.