Pogba was targeted after his second half penalty kick was saved by Wolves goalkeeper Rui Patricio during the Premier League game.
He is the third player, after Chelsea’s Tammy Abraham and Reading’s Yakou Meite, to be racially abused on social media in the past week after failing to score from the penalty spot.
In a statement, United said that those responsible for the abuse “do not represent the values of our great club.”
“Everyone at Manchester United is disgusted by the racial abuse aimed at Paul Pogba last night and we utterly condemn it,” the club said in a statement.
“The individuals who expressed these views do not represent the values of our great club and it is encouraging to see the vast majority of our fans condemn this on social media also.
“Manchester United has zero tolerance of any form of racism or discrimination and a long-standing commitment to campaigning against it through our #AllRedAllEqual initiative.
“We will work to identify the few involved in these incidents and take the strongest course of action available to us. We also encourage social media companies to take action in these cases.”