The 24-year-old actor was injured while shooting the action-adventure sequel on March 18.
Sources say he was in a harness on top of a moving vehicle when he was pulled off the vehicle unexpectedly and hit by another vehicle.
Production on the film was shut down in March in order for the actor to recover, with Fox believing it would take only a few weeks and scheduling a May 9 resumption.
Insiders say O'Brien's injuries are more severe than first believed.
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"His injuries are very serious, and he needs more time to recover," said O'Brien's publicist, Jennifer Allen.
"The resumption of principal photography on Maze Runner: The Death Cure has been further delayed to allow Dylan O'Brien more time to fully recover from his injuries. We wish Dylan a speedy recovery and look forward to restarting production as soon as possible," said a statement from Fox.
Wes Ball is directing the third film in the trilogy, in which O'Brien's character, Thomas, embarks on a mission to find a cure to a deadly disease known as the "Flare.