They were also pitted against Serie A champions Juventus in the group stage.
With Manchester City and Juve also avoiding each other until the last four, some United fans are suspicious that the draw was manipulated.
Twitter user @TheLocalMaliki claimed: "Barcelona united what a fix man."
Maxwell added: "Who fix this draws, how can Manchester United play Messi."
Other supporters feel the club's fortune is against them, given the horror run of cup opponents.
Twitter user Tяυsτ №¹-Yahya™ said: "What’s been happening this season? We’ve had Chelsea and Arsenal in the cup, had Juventus in our group stage and now PSG and now Barca whilst we’ve had 10 injuries in between that.
Ang Shang Le added: "Why are we always getting big clubs?? FA cup as well ffs."
"If we win a trophy this season i’m having a party ffs."
Former Barcelona midfielder Cesc Fabregas believes his former side will go all the way to the Madrid final and win the competition for a sixth time.
The Spaniard stated: "Barca are winning it."
United will be seeking revenge for defeats in the 2009 and 2011 finals to Barcelona, who on both occasions were managed by Pep Guardiola.
However, many fans are concerned the tie could be the end of the road for United.
Okc wrote: "Our journey now comes to an end."
Joseph Chorlton stated: "Could we not have no one?"
Paul Scholes struck the winner the last time United beat Barcelona in a competitive game - on the way to the club winning the trophy for a third time in 2008.