Ferdinand was at the stadium working as a pundit as Wolves were beaten 2-1 by United in the Premier League on Sunday afternoon.
The match saw the return of fans to the ground, with a crowd of 4,500 Wolves supporters in attendance.
During the game, Ferdinand posted a message on Twitter which said: “The last couple weeks, it’s been unreal to see fans back.
“However to the Wolves fan who has just been thrown out for doing a monkey chant at me. You need to be dismissed from football and educated.
“Come meet me and I will help you understand what it feels like to be racially abused!”
A subsequent tweet from Wolves said: “We are deeply sorry Rio.
“This person does not represent our club, our supporters or our values. We can confirm that this individual has been arrested by @WMPolice who we will support to ensure that the strongest action is taken, including a lifetime ban from our club.”
West Midlands Police said in a tweet: “A 31-year-old man has been arrested at the @Wolves v @ManUtd match this afternoon after a racist gesture was directed at @rioferdy5.
“We will not tolerate football hate crime.”
Elsewhere, audible boos were heard at Villa Park when Aston Villa and Chelsea players took the knee before kick-off.
While it was drowned out by applause for the gesture in the fight for equality, defender Tyrone Mings questioned the education of those supporters who did not agree with the pre-match ritual.
Mings said on Twitter: “A great win to finish. (It) was brilliant to have our family and the fans back at VP.
“To anyone that booed us taking the knee, have a look at yourself and ask if you truly support equality and equal opportunity for the black players on the pitch. It’s tiring. Educate yourself.
“There was also a lot of applause by the way and to you lot, I love ya’ll. Thank you.”