The killed victims include three women, four young children and two babies, said family member Alex Lebaron of Mexico. He said all nine were dual US-Mexican citizens.
The victims were "all shot dead while in vehicles while driving," LeBaron told CNN.
Investigators believe three vehicles traveling between the Mexican states of Sonora and Chihuahua were ambushed by criminal groups Monday night, Mexican authorities said.
"Women and children (between 14 years and 10 months) were killed, burned alive," Lebaron said. "Mothers screamed for the fire to stop."
The group was heading from Bavispe, Sonora, to Janos, Chihuahua, said Chihuahua Attorney General Cesar Penny
Security Secretary Alfonso Durazo said the attack could be a case of mistaken identity of "conflict groups in the area."
7 injured children are now in the United States
The attacks appear to be members of a fundamentalist sect that is separate from the Church of Jesus Christ of Latter-day Saints, a spokesman for the LDS Church said.
"That sounds like a terrible and tragic thing," spokesman Eric Hokin told CNN. "From what I can understand, these were members of a polygamist sect, not members of the Church of Jesus Christ of Latter-day Saints.
Seven children injured in the ambush were flown from Mexico to Douglas, Arizona for transportation to hospitals in Tucson, LeBaron said.
The state of Sonora, Claudia Arellano, said she was outraged by the attack.
"As a mother, I feel angry, despised, and deeply in pain for the frightening events in the mountains between Sonora and Chihuahua," she tweeted.
"I don't know what type of monsters would dare hurt women and children. As a manager, you have all my cooperation, so that this will not go unpunished and the parties responsible will pay."
The State Department is aware of the attack, a spokesman for the agency said.
"When an American citizen is missing or traveling abroad, we engage with local staff at multiple levels and provide all appropriate consular assistance," the spokesman said.
A region marred by violence
As the Mexican authorities fight violence in the region, the number of killings continues to increase.
Last year, Mexico witnessed the highest number of homicides – 33,000. And 2019 is about to break that record.
Now, the tribulation of the last widespread slaughter has spread to two countries.
Arizona resident Leah Stadden said her relatives were among the victims of an ambush on Monday.
"Their car is burned and there are bullet holes all the time," Studden tells CNN's CNTV correspondent.
"I think a lot of us are just silent. It's just terrifying."
Mohammed Taufek, Chandler Thornton and Daniel Burke contributed to this report.