Originally Published: 16 NOV 22 13:57 ET

Updated: 16 NOV 22 19:10 ET

By Stella Chan, CNN

(CNN) -- Jay Leno has undergone one surgery for his burn injuries and will undergo a second procedure later this week, according to his physician.

Leno, an avid car collector, had been working underneath a vehicle on Saturday when he was burned by a gasoline fire, Dr. Peter Grossman, who is treating the former "Tonight Show Host," said during a press conference Wednesday.

"When got pulled out from the area underneath the car, it was noted that he had pretty significant burns to face and hands," he said.

"His burns include his face, his hands, and his chest, the burns are fairly significant," Grossman noted.

Leno was first taken to a local hospital and then was transferred to the Grossman Burn Center in Los Angeles after the incident.

Leno's wife has been by his side and "obviously very concerned," the doctor said. His injuries are a mixture of second-degree and possibly some third-degree burns, according to Grossman.

"Some of the burns to the face are a little deeper and a little more concerning. Right now they're in that progression of somewhere between deep second and third-degree burns to the face. We're hoping we can keep them from progressing by using these alternate treatments, including good wound care and hyperbaric oxygen and aggressive surgical management," he explained.

"He's Jay leno, he's walking around, he's cracking jokes," he said, noting the comedian is "incredibly kind" to the hospital staff.

"His injuries are serious, his condition is good," he said. "I do anticipate him making a full recovery."