Dogs, trained to sniff out flare guns or drugs, were at the ground along with riot police for the tie's second leg.
Police said the men were being held on suspicion of offences including public order, affray and criminal damage.
Earlier, the force said it was ready for the 75,000 fans at the ground, and that any violence would be dealt with straight away.
Supporters had to walk through knife-detection arches and police had warned people "not to bring anything unusual" to the game - otherwise such items would be confiscated.
United won the match 3-1 to progress to the finalTrouble flared up after the first leg of the semi-final at the City of Manchester Stadium last week, when City beat United 2-1.
In total, there have been 29 arrests in connection with suspected violent disorder offences at that match.
Eleven of them were made on Tuesday and Wednesday after a CCTV image appeal by the force.
Assistant Chief Constable Ian Hopkins said: "We have been working hard with both Manchester United and Manchester City to ensure it is an enjoyable evening for all those supporters who attend.
"I am sure many will be wanting to have a laugh and a joke at others' expense, but as long as that does not spill over into violence."
Manchester United won the game 3-1 to progress to the final.