Ibrahimovic went off at half-time in United’s Boxing Day draw against Burnley, but Mourinho did not divulge the nature of the injury that will keep the former Paris Saint-Germain star sidelined throughout January.
“Zlatan one month out,” Mourinho told BT Sport following Saturday’s 0-0 draw against Southampton.
Ibrahimovic had only recently got back into the United team after missing the first half of the season while he recovered from a serious knee injury suffered in April.
With Ibrahimovic out for a prolonged period, Mourinho could have done without Belgian forward Lukaku being stretchered off in the first half against Southampton after a clash of heads with Wesley Hoedt.
He lay prone on the pitch barely moving while he was treated by medical staff for five minutes.
Lukaku remained conscious and was eventually carried off wearing an oxygen mask.
But Mourinho claimed Lukaku wasn’t seriously hurt.
“That’s football,” Jose Mourinho told MUTV. “He was just unlucky. I think the Dutch central defender goes with him for the ball and it’s unlucky for Romelu and unlucky for Hoedt.
“It was nothing aggressive and, hopefully, nothing important. But the first consequence is he didn’t play for the rest of the game.”
United’s match is away to Lukaku’s former club Everton on Monday, New Year’s Day.
Mourinho’s men will go into that match on a run of three successive league draws.
The United boss felt his team should have been given a penalty for handball against Southampton and he took a swipe at referee Craig Pawson.
“I think it is also a frustrating afternoon for Craig because he’s a fantastic referee, one of the most promising referees in Europe. I feel bad for him,” Mourinho said.
“We missed easy chances but there was a clear penalty that wasn’t given.”