A photograph of the fan with the number 97 on the back of his white shirt, under the words 'Not Enough,' was widely shared on Twitter.
The slogan was, according to some Twitter users, a reference to the 97 Liverpool fans who lost their lives as a result of the Hillsborough tragedy at the 1989 FA cup semifinal.
The Metropolitan Police tweeted that the supporter had been taken into custody on suspicion of a public order offence.
Sharing a tweet by a Liverpool FC fan account called the Kop Watch, the Met's events Twitter account said: "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."
The Metropolitan Police confirmed to the BBC that the arrest was solely due to the shirt worn by the fan but would not confirm that it was because of its alleged reference to the disaster.
Former Liverpool player Stan Collymore said on Twitter: "Struggling to find why someone would buy a shirt, then get numbers and words printed on it to then display it at a football match. Who'd print it?
"This isn't partisan fandom, it's celebrating tragedy that today, now, hurts so many."
Police also said they were looking at CCTV footage after an object was thrown towards a Manchester United player in the first half of the match.
Premier League champions City won the final 2-1.