The 55-year-old, known for performing his own death-defying stunts, was injured as he attempted a jump between buildings while attached to cables but fell short and slammed into a concrete wall.
US trade press reported that Cruise was left with a badly-damaged and possibly broken ankle after the accident on Saturday in central London, footage of which went viral.
"Mission: Impossible 6" -- co-starring Simon Pegg, Henry Cavill, Rebecca Ferguson, Angela Bassett and Alec Baldwin -- is due for release July 27 next year.
The crew has two more months of filming scheduled, according to the Hollywood Reporter, and the original October wrap date has been moved back to Christmas.
Variety magazine, citing several unnamed sources, said the delay could be as long as three months and quoted an "individual close to the production" who said Cruise may have broken his ankle in two places and hurt his hip.
Paramount, the studio distributing the film, and Cruise's representatives did not immediately respond to a request for comment and it was not clear how any delay would affect the rest of the cast.
Cruise is admired in the industry for his adventurous attitude to filmmaking, which over the years has involved some hair-raising moments on set.
Annabelle Wallis told the CinemaCon convention in March the star convinced her to join him in a terrifying zero gravity plane crash stunt, when the scene could easily have been filmed in front of a green screen.
The shoot involved 64 takes simulating zero gravity during four high altitude flights over two days.
"Tom is renowned for making sure that the audience gets the most out of their cinematic experience," Wallis, 32, told an audience at the annual Las Vegas gathering.
"We jump off buildings and towns explode, and Tom really does it all, and he insists his cast do it too," added Jake Johnson, 39, who plays Cruise's sidekick in "The Mummy."
"Yes, I got hurt. My character dies, I almost died. We'd do a stunt and it would hurt, and I'm like, 'I think something went wrong because it hurt' and he'd go 'Well yeah -- we jumped off a building, dummy.'"
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