The supporter was pictured on social media in a United away kit that had the number 97 on the back, along with the words "not enough".
The number is a reference to the amount of Liverpool fans that were killed in the disaster at Sheffield Wednesday's stadium in 1989. There remain questions as to how the shirt was printed.
The Met police have since confirmed that the supporter was arrested after the photograph was brought to their attention.
They wrote on Twitter: “We are aware of this and have worked proactively with officials at @wembleystadium to identify the individual. He has been arrested on suspicion of a public order offence and taken into custody.”
It has now been confirmed that the person involved has been charged by police, with a Met Police statement reading: "A man has been charged after being arrested during the FA Cup final at Wembley Stadium."
"James White, 33 (22.01.1990), of Warwickshire was charged on Sunday, 4 June with displaying threatening or abusing writing likely to cause harassment, alarm or distress.
"He was bailed to appear at Willesden Magistrates' Court on Monday, 19 June.
"He was arrested after being seen wearing a shirt which appeared to refer in offensive terms to those who died in the Hillsborough tragedy."
A statement from the Hillsborough Survivors Support Alliance on Twitter thanked the FA, the Met Police and Wembley's security staff for dealing with the fan so quickly and also hoped that his arrest would deter others from similar acts.
They said: “Let this be a warning to anyone else thinking of doing anything similar. And that goes for using any tragedy.”
They signed off their statement by calling for strong action, saying: "Let's hope the justice system can be as swift for this act of hatred. We would also like to thank the messages of support that we have received from all genuine Manchester United fans, and fans from other clubs for their support."
The FA has previously called for an end to so-called tragedy chanting, amid offensive songs about Hillsborough, the Heysel stadium disaster, and the Munich air crash.