He was found unconscious and rescued by a photographer on a personal watercraft.
Trette was airlifted to a hospital where he remains in a medically induced coma.
His brother, Bobby Trette, said he is showing improvement.
"He actually grabbed the nurse's hand when she asked," Trette said. "That's a very good sign and we're just hoping he's going to live. We're just not sure about the brain functions."
Family members said Trette is an experienced surfer who has tackled big waves in other parts of the world.
He grew up surfing in Orange County, but Trette's brother said it was his first try at Mavericks.
Trette is one of seven children.
The Associated Press contributed to this report.