The sport is known as pankration and combines skills from boxing, wrestling and various martial arts.
Assemblywoman Susan Bonilla (D-Concord) says it puts children at risk of serious injury.
Pending legislation from Bonilla would authorize the California State Athletic Commission - which already oversees full-contact boxing, kickboxing and mixed martial arts for adults - to establish regulations for youth pankration competitions.
Yet some coaches and parents are wary of the legislation, which they say is too vague and could restrict competition. They say the sport has been misrepresented as more dangerous than it actually is.
While the sport has evolved and includes a set of safety-conscious rules, the recent popularity spike and resulting media attention have caused skepticism among California officials about the welfare of young competitors. The athletic commission halted competitions in July so officials can examine whether a minimum age should set for participation and other standards.
Her bill, AB1186, specifically excludes light contact karate, tae kwon-do and judo from receiving additional oversight. Athletic commission officials say they are not aware of other states that have established regulations for youth pankration.
The legislation could come up for a vote by the full Senate this week and, if approved, would head back to the state Assembly for a final vote before it could go to the governor's office.
The Associated Press contributed to this report.