Stanton went up for a rebound against Nakia Sanford while running drills with the team Monday and took an elbow to the nose, breaking it in two places, TMZ reported Thursday.
The mayor was treated at a local hospital and released.
"Injuries are just part of the game -- they're battle wounds," Stanton said in a statement.
Mercury Coach Cory Gaines described the incident as "hilarious."
"You can't script it any better," he said.