The 58-year-old suspect from the North Wales area was held on Saturday evening, hours after the game at Anfield.
Earlier, a television image capturing a Liverpool fan making an alleged racist gesture during the clash was distributed on social networking websites sparking a number of complaints to the force.
A Merseyside Police spokeswoman said: "A 58-year-old man from North Wales who was arrested on suspicion of a racially aggravated public order offence yesterday following the Liverpool and Manchester United match has been released on police bail pending further inquiries."
It was the first game between the rivals since the eight-match ban imposed on Liverpool striker Luis Suarez after the FA found him guilty of racially abusing United defender and captain Patrice Evra.
Before the match, in which Liverpool triumphed 2-1, the stadium announcer warned supporters that racist and homophobic behaviour would not be tolerated.
It is understood that home supporters found guilty of such offences inside the ground would be subject to life bans from the club.
