According to police, the accident occurred in southeastern Albuquerque just before noon Sunday when the driver of a rented SUV ran a red light. The driver, whom an off-duty officer identified as Jones, ran from the scene but then returned for the cash before fleeing again, police said.
"Witnesses stated he shoved the cash into his pants and ran north," the report said.
Albuquerque police were seeking an arrest warrant for Jones on Monday, saying he would likely face a felony charge of leaving the scene of an accident since the woman broke her arm in the crash.
Police said they have been unable to reach Jones or his lawyer.
Officers found a pipe with marijuana in the SUV as well as MMA and rental car documents in Jones' name, according to the police report.
His agent, Malki Kawa, did not immediately respond to an email from The Associated Press.
Jones (21-1) is scheduled to defend his title against Anthony "Rumble" Johnson at UFC 187 in Las Vegas on May 23, headlining one of the promotion's biggest shows of the year.
"We are in the process of gathering facts and will reserve further comment until more information is available," the UFC said in a statement.
Although he is widely considered the world's best pound-for-pound mixed martial artist, Jones has endured legal problems and questionable behaviour as champion.
Jones was arrested in 2012 after crashing his Bentley into a telephone pole in Binghamton, New York. He had his driver's license suspended after being charged with DWI, but did no jail time.
Last August, Jones and challenger Daniel Cormier were involved in a brawl in the lobby of the MGM Grand casino while appearing at a promotional event. Jones was fined $50,000 and ordered to do community service by the Nevada Athletic Commission.
In early December, Jones tested positive for metabolites of cocaine while training for his bout. Jones was allowed to compete because the test was conducted out of competition, and he beat Cormier at UFC 182.
When the failed drug test became public, Jones publicly apologized for a "mistake," but spent just one day in a drug rehabilitation centre before checking himself out.
Jones has defended his belt eight times since becoming the youngest champion in UFC history in March 2011.
Jones is a native of upstate New York, but lives in New Mexico and works under prominent local trainer Greg Jackson. Jones has two brothers who play in the NFL.
Albuquerque is a hub for MMA fighters who train at Jackson's gym and use the city's high altitude to prepare for bouts.
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