Fury says he needs to deal with his "medical treatment and recovery."
Jason Kenny and Laura Trott both won gold medals.
The boxer lost to Russia's Vladimir Nikitin after a controversial judge's decision.
The Olympic gold medallist competes Tuesday.
The middleweight boxer is the cousin of Liverpool striker Robbie Fowler.
Muhammad Ali's match with Japanese wrestler Antonio Inoki has often been seen as a freak show. It was anything but.
Later, thousands of people will attend a memorial featuring eulogies by former U.S. President Bill Clinton and comedian Billy Crystal.
"The passing of Muhammad Ali has made us all feel a little more alone in the world."
The Real Madrid forward earned $88 million in 2016.
The boxing icon's funeral will take place in Louisville on Friday.
The boxing icon died on June 3 aged 74.
Hometown will host a procession followed by a service with eulogies by President Bill Clinton, Bryant Gumbel and more.
The self-confessed 'fat man' has gone on a health kick.