Jones was arrested on suspicion of leaving the scene of an accident involving personal injuries -- a felony. He was booked at the Metropolitan Detention Center and released on bond a short time later, Bernalillo County officials told the Associated Press.
According to the police report, an off-duty officer who witnessed the Sunday morning crash said Jones, who was driving a sport utility vehicle, ran a red light and crashed into another vehicle. Jones then ran away from the scene only to return a short time later to retrieve cash from the SUV before fleeing again.
The pregnant woman, who was in the other vehicle, was transported to the hospital with minor injuries.
Police reported they found a pipe with marijuana in the SUV being driven by Jones in addition to rental car documents.
Jones (21-1), the current UFC light-heavyweight champion, is scheduled to fight Anthony Johnson (19-4) at UFC 187 in Las Vegas on May 23.
"We are in the process of gathering facts and will reserve further comment until more information is available," the UFC said in a statement.
Jones has had prior run-ins with law enforcement.
Three years ago, he pleaded guilty in New York to misdemeanor driving while intoxicated. In December, he tested positive for cocaine but still fought on Jan. 3. He later spent one night in a drug treatment facility.
Jones is one of the most popular MMA fighters in the country. He won the light-heavyweight title in 2011, becoming the youngest champion in UFC history. He's ranked No. 1 by various media outlets for his weight class.
Jones, who is from Endicott, N.Y., and was a state champion wrestler in high school, is praised by fight enthusiasts for his wrestling ability.