The La Liga side dropped down into the competition after finishing third in their Champions League group, behind Bayern Munich and Inter Milan, along with the likes of Juventus and Ajax.
United are involved in the knockout round after coming second in their Europa League group, and the tie neutrals wanted materialised during Monday’s draw in what is the worse-case scenario for both sides.
Following their Champions League exit, a deep European run is expected from Barcelona but they now face a big test just to make the last-16.
“It is the most difficult opponent once again, but we will look forward to it,” Xavi told reporters.
“They are a historic side, they have grown a lot with the arrival of Ten Hag, they have great players. It’s the worst draw we could have got. Once again no luck.”
The first leg of the tie will take place at the Camp Nou on February 16, with the return fixture at Old Trafford a week later.
Barcelona sporting director Jordi Cruyff, who spent four years as a United player, was unsurprisingly excited about the draw, though admitted it would have been better had the two sides met later in the competition.
“Two big clubs, worldwide fanbases, a lot of pressure, so it’s gonna probably gonna be the most important match of that week,” Cruyff told BT Sport.
“I think for fans, especially for neutral fans, it’s an amazing draw. I think for fans of both clubs, it’s a draw that they will love, but again I think it’s the toughest draw at the moment.
“You prefer those draws further down the line but on the other hand it’s beautiful and for a lot of spectators probably the reason to stay at home those two nights to watch a magnificent football game with a lot of extra things because we have a lot of recent history, a lot of games in the Champions League of course.”
