Young was targeted on Twitter following United's 3-0 quarter-final second-leg defeat on Tuesday.
The foul abuse of Young brought swift condemnation from United, who
said in a statement: "Manchester United utterly condemns racist social
media comments posted around yesterday's Champions League fixture.
"We are working to identify individuals involved and we will take the strongest possible action we can against them.
"There is no place for racism within our game, or in society as a
whole, and we are committed to working to make football free from all
forms of discrimination."
The 33-year-old was partially at fault for Barcelona's first goal as
his clearance was blocked, leading to Lionel Messi scoring as the hosts
went on to win 4-0 on aggregate.
Anti-discrimination campaigners Kick It Out called upon the social media platform to act following a series of incidents.
The organisation said via its own Twitter account: "Yet another black
player, this time Ashley Young, targeted with racist abuse on social
media after tonight's Champions League game.
"Again, we're left asking @TwitterUK the same question - when will
you take serious action to tackle the rampant discrimination on your
Twitter was swift to respond, confirming that the posts concerned had
violated its abusive behaviour policy and that the account holders
would be required to remove them before they could tweet again.
Premier League stars Mohamed Salah, Danny Welbeck, Raheem Sterling,
Michy Batshuayi, Pierre-Emerick Aubameyang and Moussa Sissoko have all
received abuse over the same platform in recent years.
England's black players were subjected to repeated chants during
their Euro 2020 qualifier in Montenegro last month, while Tottenham
defender Danny Rose revealed recently he has "had enough" of racism in
football and "can't wait" to quit the game.