The shooting at the Target parking lot happened Monday afternoon near Highway 18 and Dale Evans Parkway.
Investigators identified the suspect as 41-year-old Dearld Wicker of Apple Valley and obtained a warrant for his arrest.
Authorities tracked Wicker down in the 25000 block of Flathead Road on Tuesday around 6 p.m. Tuesday. Deputies said Wicker was armed with a handgun when they made contact with him.
At some point, a deputy-involved shooting occurred. Wicker was wounded and transported to Loma Linda University Medical Center in unknown condition.
The victim who was shot outside the target was expected to survive.