The 34-year-old fighter had been scheduled to turn himself in on Friday to begin serving a 90-day sentence imposed last month.
A judge said she weighed Mayweather's contractual obligations to the fight set for May in Las Vegas against an as-yet unnamed opponent.
Mayweather's lawyer pleaded with the judge to allow Mayweather to fulfill commitments regarding the fight, emphasising the economic benefit to Las Vegas when Mayweather fights.
Mayweather pleaded guilty on December 21 to a reduced battery domestic violence charge and no contest to two harassment charges.
The plea deal saw prosecutors drop felony and misdemeanor charges that could have gotten Mayweather 34 years in prison.