The Briton told ESPN television after his 10th-round stoppage of title challenger Derek Chisora on Saturday that his right elbow was the problem.
"I’ve got some hand problems and I’ve got to maybe have some surgery on my elbow but after that, I’m ready for anybody," he said.
"I had the left (elbow) done back in October (2021) after the Wilder III fight, so I’ve got to have it done. It will take about six to eight weeks to heal.
"We’ll see when we'll be ready for this fight, we’ll see when it can be made."
Fury said his promoters Bob Arum and Frank Warren had talked of a potential clash with Usyk, the WBA, IBF, WBO and IBO champion, towards the end of February or in March.
Adding to the uncertainty, the undefeated WBC champion told reporters at a post-fight news conference that he felt great and was looking forward to a "massive 2023".
Fury taunted Usyk, who was ringside for the fight at London's Tottenham Hotspur Stadium, and challenged him to get the fight on.
The Briton also said he would take on his undefeated compatriot Joe Joyce, the 2016 Olympic super-heavyweight silver medallist, at Wembley if the Usyk fight could not be made.
"I just think I can beat anybody. There's no stopping me, I'm on a roll. I'm going to be match fit going into the next fight, can't wait," he told ESPN.
"Whoever's next will get knocked out as well."
