The American boxer is being sued over statements accusing the Filipino superstar of taking performance-enhancing drugs.
The two, considered the best fighters, pound-for-pound, in the world, have failed to reach terms on what could be the richest bout in boxing history.
Federal magistrate Judge Robert Johnston denied an emergency motion on Thursday that would have allowed Mayweather to delay testifying.
He was ordered to start testifying in Las Vegas on Friday, June 17.
Mayweather claimed he needed to concentrate on his September 17 fight against Victor Ortiz.
Mayweather also faces felony charges stemming from a domestic argument and misdemeanour harassment and battery charges in separate cases.