The 30-year-old has been replaced by former British champion Lee Purdy, who will take to the ring on September 8 against Carrasco, who has recorded 13 knock-outs in 16 wins.
Barker tweeted: "Absolutely gutted I've had to pull out of this fight. I've trained my nuts off and was feeling right on song. Life goes on."
Promoter Eddie Hearn said: "It's a fantastic opportunity for Lee and it promises to be a great fight against Carrasco, who brings a great knockout record to London.
"Lee is always in exciting fights and I'm sure that this occasion will bring the best out of him and the fans will love it, you only have to watch Carrasco on the internet to see what kind of war this is going to be.
"I am gutted for Darren as he's been looking great in training and I know he was ready to get back to what he does best. The only good news is that it is a new injury rather than an aggravation of an old injury and we hope he will be back in action very soon."
Barker has been told that he will not be able to train for a month.