Lukaku, who has scored 15 times this season, had played every minute in the Premier League before being taken off on a stretcher against Southampton on Saturday, following a clash of heads with Wesley Hoedt.
The Belgian missed Monday’s trip to his former club Everton and he is set to sit out for the FA Cup third-round tie with Derby on Friday too.
Speaking prior to the clash with the Toffees, Mourinho told Sky Sports: “I would say a week [out for Lukaku] .
“It’s nothing really important — just a little protection, but no problem.”
There are 10 days between Derby’s visit to Old Trafford and United’s Premier League home clash with Stoke, when Lukaku may be available again.