James suffered the fracture when hit by Dikembe Mutombo's elbow in the Houston Rockets' 98-87 win over the Cavaliers Wednesday.
The Cleveland guard is "officially listed as day-to-day," a report from the team said.
"He will be fitted for a custom protective facial mask as soon as his facial swelling subsides and is expected to wear the mask upon his return to the court for play, as needed."
"Injuries are a part of the game," Coach Paul Silas said after the loss to Houston. "When you lose your best player, it is always hard to recover."
The Cavaliers next play Monday at Charlotte.
James, who turned 20 Thursday, is averaging 24.4 points, 7.2 assists and seven rebounds in 29 games this season.