The Belgian striker, who is United's top scorer with 10 Premier League goals, suffered a head injury in the draw with Southampton as a result of a collision with Wesley Hoedt.
Lukaku was taken off on a stretcher and given oxygen. However, he did not need to go to hospital and was instead examined by United's medical staff.
However, Lukaku should be able to return for the visit of struggling Stoke City on January 15.
"I would say a week [out for Lukaku]," Mourinho told Sky Sports.
"It's nothing really important - just a little protection, but no problem."