Kuroda was released from the hospital on Sunday and was cleared to fly home with the team.
"Amazingly, things look really pretty good," Dodgers head athletic trainer Stan Conte said. "The fact that he didn't lose consciousness is a very good sign."
Conte says a CAT scan was negative and Kuroda's only symptom Sunday was a mild headache. He will undergo further tests by neurologist Dr. Vernon Williams on Monday.
A shot off the bat of Arizona pinch-hitter Rusty Ryal caught Kuroda on the right side of his head with Los Angeles leading 3-0 in the sixth inning. The 34-year-old Kuroda crumpled to the mound, clutching his head, as the ball deflected into the seats behind first base.
"One of the first things he asked out there was if anybody caught the ball out there, if it was an out," Conte said.
All eight Dodgers fielders stood on the mound as trainers tended to Kuroda, who was placed on a stretcher and loaded onto a cart. He raised both of his arms as the cart rolled off the field, and was taken to St. Joseph's Hospital for tests.
Ryal was awarded a ground-rule double, and James McDonald relieved Kuroda.
Los Angeles led 3-0 at the time of Kuroda's injury, but the Diamondbacks rallied against the Dodgers' bullpen.