Photo: AFP
The talismanic Swede, 35, had to go off after damaging his right knee late in the game at Old Trafford and may not play again this season, while United also lost centre-back Marcos Rojo.
United prevailed courtesy of an extra-time strike by Marcus Rashford, which secured a 3-2 aggregate success, after Henrikh Mkhitaryan's opener was cancelled out by Sofiane Hanni.
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"I don't think they are easy injuries, but I prefer to wait until all the tests are done and then speak. But the news is fairly negative I think," United manager Jose Mourinho told BT Sport. "It is an important title and we have to keep going. Today showed how difficult it is. We are not expecting anything easy in the semi-finals."
The scrappy, sapping victory means Mourinho's side remain on course to claim the only major trophy missing from the club's collection.
But the injuries to Ibrahimovic and Rojo could prove costly, particularly with United having re-energised their push for a top-four finish in the Premier League by brilliantly beating Chelsea.
Ibrahimovic's injury occurred late in stoppage time, his right knee bending the wrong way as he landed following an aerial challenge in the Anderlecht box, leaving him grimacing on the deck.
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The former Paris Saint-Germain striker, scorer of 28 goals this season, was able to hobble down the tunnel, aided by medical staff, but United's fans will fear they have seen the last of him this season.
It cast a shadow over United's evening, but Rashford's superb 107th-minute strike ensured they took up a place in the last four.
Elsewhere, Ajax reached their first European semi-final in 20 years with a 4-3 aggregate win over Schalke after extra time.
Leon Goretzka and Guido Burgstaller scored in the space of three second-half minutes to cancel out Ajax's advantage from the first leg.
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Daniel Caligiuri hit Schalke's third after 101 minutes thanks to Sead Kolasinac's fine cross.
But Nick Viergever quickly levelled on aggregate before Amin Younes hit a last-minute winner for the Dutch who finished the game with 10 men after Joel Veltman had been red-carded in the 80th minute.
Celta Vigo reached a European semi-final for the first time after a 1-1 draw at Genk gave them a 4-3 aggregate win over the Belgians.
In Istanbul, Lyon beat Besiktas 7-6 on penalties after the Turkish side had won 2-1 on the night to level the tie at 3-3.
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