Officers arrested 38-year-old Live Oak resident Eric Lamb in connection with the crime, which occurred around 11 a.m. at San Lorenzo Park.
Witnesses told police Lamb came riding through the park from the Dakota Street side and encountered two children.
They said Lamb started yelling profanities and threatened that he would hit them if they didn't move out of his way, according to police.
He then allegedly swerved about 7 to 8 feet from his path and deliberately struck a 3-year-old boy, knocking him down and running him over, witnesses told police.
Arriving officers found a bike tire mark across the boy's sweatshirt.
He was taken to a hospital to be treated for abrasions and bruises.
After canvassing the downtown area, officers found Lamb on Pacific Avenue and took him into custody.
Lamb was booked into Santa Cruz County Jail on charges of assault with a deadly weapon and willful cruelty to a child.
Anyone with information about the case is asked to contact the investigations unit at (831) 420-5820.