Wounded were three adults, a 16-year-old and children ages 1, 6 and 9 who were not all from the same family.
Mesa Police Chief Ken Cost said Saturday the 1-year-old child remained in extremely critical condition.
He said the other injuries ranged from minor to severe, but none were believed to be life threatening.
The names of the seven wounded people haven't been released by police.
Cost said a man was seen assaulting a woman at the same location earlier Friday night and one of the food vendors and other bystanders intervened.
Investigators haven’t tied the incident to the shooting, but also haven’t ruled it out.
Police are looking for “anyone and everyone” who may have witnessed the fight or the shooting to contact police, Cost said, adding that any details, videos or photos might lead to an arrest.
“They shot children and it’s unacceptable,” Cost said. “You need to come forward and do the right thing ... Help us bring justice to these family members who had their children shot.”