The unbeaten 26-year-old (15-0-KO2) had been due to defend his IBF title on the undercard of Carl Frampton v Nonito Donaire in Belfast.
McCullough (18-4-KO11) said: “It’s obviously disappointing to have prepared for this long and then be unable to fight on the night but I’ll be back.
“Hopefully Jono can heal quickly and we can move the fight rather than cancel it altogether. I still want to face him so hopefully it can happen at the first available opportunity.”
Carroll was last seen in November 2017 when he produced an eye-catching early stoppage of Humberto de Santiago – also in Belfast.
McCullough fought on the same card at The SSE Arena that night; halting Josh Baillie in the third round.