Veilleux returned to Minnesota late Saturday evening after spending Friday night in a Detroit hospital.
According to a report in the St. Paul Pioneer Press, it's uncertain whether he'll be able to don a facemask and return to the team when it resumes play after Christmas.
Wild coach Jacques Lemaire told the newspaper it was a gruesome injury; Veilleux's nose was smashed to the side of his face and his face was cut.
"He's not in good shape," Lemaire said. "Don't count on him for a while."
Information from The Associated Press was used in this report.