Dr. Peter Grossman, a plastic surgeon and medical doctor at the Grossman Burn Center and West Hills Hospital where the former Tonight Show host was treated, said during a press conference on Wednesday that Mavis Leno is "obviously very concerned."
"She's by his side," Grossman added of Leno's wife of nearly 42 years. "They have a very close relationship, and she's doing as well as you can expect a wife who is concerned about her husband."
On Saturday, the comedian, 72, was working on a steam engine underneath a car in his garage when a fire began. Leno was pulled from underneath the car but suffered "significant" burns to his face, chest and hand.
While at Grossman Burn Center, Leno underwent a surgical excision and grafting procedure to the burned areas, his doctor explained, noting that a lot of the thickness of his skin was injured. The surgery involves removing unhealthy tissue and placing a biological skin substitute on the wounds in order to expedite healing.
During the news briefing, Grossman saluted Leno as an "ideal patient" during his hospitalization.
"He's been a remarkable kind and engaging patient," continued the surgeon. "He passed out cookies to children in the burn unit. Mr. Leno has been very open about sharing information with you."
Grossman noted, "He's Jay Leno — he's walking around and cracking jokes. He's incredibly kind to our nursing staff. He's very compliant. He's very appreciative of everyone here and really an ideal patient and one who understands the seriousness of his injury."
He confirmed the star was "in good spirits" on Wednesday following his surgery, though another procedure will be needed later this week.
"Currently, there's no evidence of nerve damage. I do anticipate him making a full recovery. Whether they'll be remnants of this injury, it's still too early to tell," Grossman said. "I'd say that his injuries are serious, his condition is good."
RELATED VIDEO: Jay Leno Says He Suffered 'Serious' Burns After Being Involved in Gasoline Fire: 'I Am OK'
Speaking out about the gasoline fire, Leno confirmed in a statement shared with PEOPLE on Monday that he's recovering after obtaining "serious burns."
"I got some serious burns from a gasoline fire," he said. "I am OK. Just need a week or two to get back on my feet."
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Aimee Bennett, a spokesperson at the Grossman Burn Center, also issued a statement to PEOPLE, confirming that Leno was being treated there after the incident in his garage.
"Jay wants everyone to know that he is in stable condition and receiving treatment ... for burns that he received to his face and hands from a gasoline accident in his garage over the weekend," Bennett said at the time. "He is in good humor and is touched by all the inquiries into his condition and well wishes. [He] wants to let everyone know he is doing well and is in 'the best burn center in the United States.'"