Villanueva said some of the recruits heard the car accelerating, and had estimated it was traveling around 35 miles (56 kilometers) an hour when it crashed into the group.
Officials said the driver, who has not been named, was taken into custody at the scene of the incident. The circumstances of the crash were under investigation, with the California Highway Patrol (CHP) taking the lead.
Initial breathalyzer tests found the driver was not drunk, Villanueva said.
"It looks like it's an accident -- a horrific accident -- but we can't know that for sure until the CHP does their investigation and reaches a conclusion based on all the evidence they still have yet to gather," he told reporters.
The LA Times cited unnamed law enforcement sources saying the driver had told officers he was sleepy, and tests were underway to establish if the 22-year-old was under the influence of any drugs.
Marijuana is legal for recreational purposes in California, and its use is widespread, particularly among younger people.
California Governor Gavin Newsom said he and his wife, Jennifer Siebel Newsom, were thinking of the injured recruits.
"Our hearts are with the Los Angeles County sheriff's recruits injured this morning while training to serve their communities," a statement said.
The group was made up mostly of recruits from the Los Angeles Sheriff's Department, but also included trainees from other nearby police forces.
They were members of a training academy, participating in a 22-week program that focuses on instruction in the use of firearms, self-defense, law enforcement driving, physical fitness and force de-escalation, as well as law and police procedures.
The Los Angeles Sheriff's Department is responsible for policing Los Angeles County, a sprawling region that is the United States' most populous county.
