Fellow Briton James DeGale, 29, who was the mandatory challenger, will now fight for the vacant title.
Froch, 37, wants to defend his WBA super-middleweight title this summer.
Talks have taken place over a potential bout against Mexico's Julio Cesar Chavez Junior in Las Vegas, or two-weight world champion Bernard Hopkins, 50, in Froch's home city of Nottingham.
Froch told BBC Radio 5 live a fight in Vegas or at Nottingham Forest's City Ground would be motivation to continue his career, although he has not ruled out retirement.
"Something needs to happen soon because if it doesn't, I will be retiring," added the boxer, who has won 33 of his 35 fights.
The four-time world champion said he felt frustrated at having to pull out of a fight with Chavez which was originally scheduled for March.
"I know what it's like to wait for a shot and I didn't want to hold James up in fighting for a world title," he said.
"James is a great fighter and I hope he can go out and win that title. Who knows... we may even meet later in the year."
DeGale earned the right to face Froch after beating Brandon Gonzalez on the undercard of Froch's Wembley fight against George Groves in May 2014.
Promoter Eddie Hearn is in negotiations for Degale to fight American Andre Dirrell for the IBF title and hopes the clash can take place on 25 April at London's O2 Arena.
"I'm making history," said DeGale. "I'm going to be the first British Olympic gold medallist to win a world title."
Carl Froch has vacated his IBF super-middleweight belt as he recovers from an elbow injury.