Cleverly was due to face the dangerous Makubu in Monaco next month, but the fight has been cancelled after the Welshman suffered an injury.
This is the second time that Cleverly has put off his ring return, with injury problems also forcing him out of a fight against Daniel Amman in November.
“He has sustained a minor injury and will not be fighting in Monte Carlo on February 1st and we are about to re-schedule a fight for him,” said promoter Frank Warren.
Cleverly is hoping to rebuild his career after his WBO light-heavyweight belt was ripped away in a crushing knockout defeat by Sergey Kovalev in August.
The 26-year-old decided to pursue titles in the division above, but must wait longer for his first fight in 2014.