The 20-time English champions will make the trip to Camp Nou on February 16 for the first leg of the contest before welcoming the Catalan giants to Old Trafford on February 23.
The winner of the contest will then advance to the knockout round of the competition.
Barcelona finished third in their Champions League group behind Bayern Munich and Inter Milan to drop into the Europa League, but Xavi's side are now flying high at the top of La Liga, while they recently won the Spanish Super Cup and are in the semi-finals of the Copa del Rey.
Man United, meanwhile, won five of their six games in the group stage of the Europa League, but it was not enough to finish ahead of Real Sociedad at the top of Group E.
The Red Devils made three signings during the January transfer window, with Jack Butland arriving on loan from Crystal Palace to boost the goalkeeping options available to head coach Erik ten Hag.
Meanwhile, Wout Weghorst joined on loan from Burnley, and Marcel Sabitzer made the move to Old Trafford on loan from Bayern Munich on deadline day.
Butland, Weghorst and Sabitzer are all in the squad, with Cristiano Ronaldo dropping out following his departure at the end of November.
Martin Dubravka is also removed from the squad, having returned to parent club Newcastle United, while Axel Tuanzebe is out following his loan move to Stoke City.
Shola Shoretire and Charlie McNeill will also not feature in the latter stages of the competition, having made loan moves to Bolton Wanderers and Newport County respectively.
Donny van de Beek is out for the season following knee surgery, but he is still in the squad.
Meanwhile, Christian Eriksen - out until at least the end of April with an ankle injury - also keeps his place.
Phil Jones has not been involved for the Red Devils this season, though, and the experienced defender is not included, while there is also no place for Brandon Williams.
Man United can add 'homegrown' players from the B list, with the likes of Anthony Elanga therefore available despite being left off the 25-man list.
Man United's Europa League squad:
De Gea, Butland, Heaton; Dalot, Lindelof, Maguire, Malacia, Martinez, Shaw, Varane, Wan-Bissaka; Casemiro, Eriksen, Fernandes, Fred, McTominay, Sabitzer, Van de Beek; Antony, Garnacho, Martial, Pellistri, Rashford, Sancho, Weghorst