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."

It is the first meeting between the sides in the competition in more than five years.
"Over the next five or six weeks, I fully expect Rangers to have the league wrapped up, so they should be the confident team going into the game.
"For me right now, I would sway towards Rangers," Boyd said.
The last match between the sides was in last season's League Cup semi-final, with Celtic emerging as 2-0 victors.
Rangers appear to be a stronger proposition on the pitch now under manager Mark Warburton.
They are on course to seal promotion to Scotland's top flight at the end of the season, leading the Championship table by 12 points.
Boyd thinks the togetherness of the Rangers squad could give them the decisive edge over Celtic, who have faltered in recent weeks under Ronny Deila despite continuing to lead the Premiership.
"They've got that close-knit unit," said Boyd, who was impressed by the 4-0 win over Dundee.
"If you look at the way they performed on Saturday, it was excellent right from the word go.
"It's going to be close. I'm leaning towards Rangers in terms of the tight-knit group. They know exactly what they are doing.
"With a steady team, there's no chopping and changing. You are going to training all week fully expecting to play, whereas you look at Celtic - with the amount of bodies they've got going into training on a Monday morning expecting to play on a Saturday, they could field three or four teams."
Former Celtic striker Scott McDonald agrees that Rangers will provide Deila's men with a much sterner challenge than they did in the League Cup semi-final in February 2015.
"Rangers now you feel are much more ready for the challenge than they were 13 months ago," McDonald explained.
"Under Warburton, they've come on leaps and bounds and the football they've played at times has been very entertaining."
The Motherwell frontman believes the return of Scottish football's most famous rivalry is great for the game.
"Without being disrespectful to all the games in the leagues and the derbies, this is the one," said McDonald.
"It's rated as one of the best derbies in the world. So to have it back on the map again is fantastic for Scottish football.
"It really needs it within the game. We're hoping for a great spectacle.
"It certainly puts it back on the map. It's a chance for both teams to sort of stamp their authority on next season, psychologically you could say, and see where Rangers are really and if they have narrowed the gap from 13 months ago or not."
Carl Froch has vacated his IBF super-middleweight belt as he recovers from an elbow injury.
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Former Rangers striker Kris Boyd has backed his old side to come out on top against Celtic in next month's Scottish Cup semi-final.