Hospital spokeswoman Katy Hillenmeyer said Kirby is in the intensive care unit.
Kirby, 43, suffered major injuries and his son Nicholas was killed when a large oak tree fell on their 2002 GMC Sierra pickup truck on Bennett Valley Road east of Santa Rosa Tuesday morning.
Kirby's 42-year-old wife, Diane Musser-Kirby, suffered minor injuries. A 5-year-old Glen Ellen girl who was riding in the back seat with Nicholas was not injured.
The tree fell on the cab of the truck, causing the most damage to the left side of the vehicle, the California Highway Patrol reported. Nicholas was sitting behind his father, who was driving the pickup.
Marin County Sheriff's Sgt. Debra Barry called Kirby "a distinguished peace officer who has served both the Sonoma County Sheriff's Department and the Marin County Sheriff's Office.
"He is well-liked and respected by his peers. We are all overcome with grief at the loss he and his family have suffered," Barry said.
The tragic accident happened on the same morning two Marin County Sheriff's Office employees, both Sonoma County residents, were identified as the winners of $75.7 million in the Mega Millions Lottery drawing Friday.
Barry said Tuesday she was returning from Hayward where the winners, Brian Cabaud and Anneliese Hansen, claimed their prize when she heard about the accident. She then drove to Santa Rosa Memorial Hospital.
"Mike and his family are in our thoughts and prayers. We look forward to his full recovery and we will stand with them through their suffering and loss," Barry said.
The Marin County Sheriff's Association has established an account for donations. It is the Kirby Family Account .11597 c/o Marin County Federal Credit Union, P.O. Box 4218, San Rafael 94913.