Riverside police said the suspect robbed a bank at gunpoint just before 6 p.m. in the 19300 block of Van Buren Boulevard and fled the scene.
The suspect then led police and Riverside County sheriff's deputies on a chase starting on the southbound 215 Freeway.
The San Diego County Sheriff's Department took over the pursuit from Riverside authorities when the chase entered San Diego County.
The suspect stopped in front of Rady Children's Hospital and is in a standoff. Officers and K-9s surrounded the suspect's vehicle, a black SUV. Rubber from at least one of the vehicle's rims was seen completely gone.
A shelter-in-place order for patients and employees has been put in place and a lockdown inside the hospital is underway due to safety concerns.
A SWAT team is at the scene.