The motion, filed Monday with Las Vegas Justice of the Peace Melissa Saragosa, comes just 12 days into Mayweather's sentence.
Mayweather's lawyers say his physical condition is deteriorating as a result of stress, alleging he is segregated from the rest of the prison population and confined to his cell 23 hours a day in an area populated by felony defendants.
The Las Vegas Review-Journal reported the motion accused the detention center of providing Mayweather's felon neighbors with better conditions, saying his celebrity status "cannot be accommodated at the [Clark County Detention Center]."
The motion said failure to release Mayweather into house arrest could prematurely end his boxing career.
Mayweather pleaded guilty to beating his ex-girlfriend in front of their children, and was sentenced to 90 days in jail. He began serving his sentence June 1. Police said Mayweather was isolated from other prisoners intentionally, for his own protection.