Saunders was stopped in the eighth round of the super-middleweight unification bout at AT&T Stadium after Alvarez landed an uppercut that left his right eye swollen and shut.
The Briton was taken to hospital after the fight and will undergo surgery on Sunday, Hearn said.
“Just at hospital in Dallas, (Billy Joe Saunders) stayed overnight,” the promoter confirmed on Twitter. “Suffered multiple fractures to orbital area and will undergo surgery this afternoon.”
Saunders was down on all three scorecards when the fight ended but had impressed in a valiant showing against the Mexican superstar.
Speaking immediately after the fight, Hearn said: “He couldn’t see. I spoke to [Saunders’ trainer] Mark Tibbs, he said he couldn’t see and he wouldn’t let him go out. He busted his eye socket.”