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.
"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.
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.
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.
Star of Sunday's 2-0 win over Chelsea, he notched the decisive goal by gathering Marouane Fellaini's knock-down, making space with a sharp Cruyff turn and firing in a low shot with his left foot.
United first went ahead in the 10th minute after a finely measured pass from Paul Pogba found Rashford wide on the left.
United were on top and it took flying one-handed saves from visiting goalkeeper Ruben to repel a header from Pogba and a Jesse Lingard curler.
- Ajax advance -
================
But United then lost Rojo -- hurt as he tried in vain to halt Frank Acheampong, with Daley Blind taking his place -- and Anderlecht levelled the tie in the 32nd minute.
Youri Tielemans's deflected shot came back off the crossbar and after a moment's confusion, Hanni put away the rebound.
Rashford rounded Ruben but knocked the ball too wide after an error by Dennis Appiah and Ruben thwarted Ibrahimovic from substitute Fellaini's header.
A corner from Mkhitaryan fell for Pogba on the edge of the six-yard box, but he skied his volley into the Stretford End.
Freed by Michael Carrick, Ibrahimovic shanked wastefully wide.
Teed up by Ibrahimovic's scooped pass, Rashford found the side-netting.
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.
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.
Disclaimer: No Business Standard Journalist was involved in creation of this content
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
