In a statement on Facebook, the Fairfield Police Department said the crash happened around 2 p.m. Sunday on the 2400 block of West Texas Street.
When officers arrived, they found the child and he was taken to a nearby hospital where he later died.
Police say the driver left the scene after hitting the boy and left his car at the site of the crash.
Around 6 p.m., the suspect, identified as Cirilo Martinez Telles, 32, returned to the scene and was arrested on a warrant for vehicular manslaughter and felony hit-and-run causing death.
The Solano County District Attorney is now reviewing whether additional charges, including murder, DUI and probation violation, will be filed against the suspect in connection to the child's death.
Police believe alcohol impairment was involved in the crash.
The Fairfield Police Department expressed condolences to the child's family on Facebook Sunday night.
"Anytime a child is involved, and tragically dies, the investigation negatively impacts all involved. Our thoughts are with the family of the 2-year-old boy," the department said.
The child has not been identified by authorities.
Police have only said Martinez-Telles is the boy's uncle.