Curran (17-4) suffered a fractured orbital bone in the third round of sparring Tuesday morning at his gym in a suburb outside Chicago, according to the promotion.
"It's an incredibly frustrating injury, especially to happen so close to the fight, but these things happen," Curran said. "I can honestly say I'm in the best shape of my life, but injuries happen and once I heal up, I'm going to continue to train and come back stronger than ever to defend the Bellator featherweight title."
Since moving down from lightweight, Curran is 4-0 at 145 pounds, including a convincing title win over Joe Warren in March.
Curran's first defense of the belt will be delayed for several months. The bantamweight tournament final between Marcos Galvao and Luis Nogueira will take the top spot on the card. Light heavyweights Travis Wiuff and Atilla Vegh will also vie for a tournament crown.
"First and foremost I feel horrible for Pat, he's been looking forward to this fight pitting two of the best 145 pounds in the world against each other for months," Rebney said. "Pat always elevates his game as the stakes get higher and higher. Right now the focus is Pat healing and getting back to 100 percent and we will get that fight rescheduled as quickly as Pat's health will allow us to."
When he returns, Curran has Freire (17-1) and Daniel Straus (20-4) waiting in the wings. Both fighters won Bellator tournaments to earn their shot.