The 25-year-old was arrested on suspicion of grievous bodily harm with intent, violent disorder and burglary, police said.
Officers took the man into custody after bringing a warrant to an address on the Wirral in Merseyside on Tuesday.
A police statement said: “The arrest was in relation to a breach of the Manchester United grounds and an officer who was left with a broken eye socket, broken nose and a slash to the face after an object was thrown at his face. He continues to receive medical treatment for his injuries.”
GMP said a number of officers were injured in the protest which saw about 1,000 Manchester United supporters rally outside Old Trafford, and about 200 outisde the Lowry Hotel in the city centre, ahead of the team’s match against Liverpool on Sunday 2 May.
Protesters gathered in the wake of the European Super League fiasco against the Glazer family’s ownership of the club, with fans storming the pitch ahead of kick-off.
The match had to be postponed after flares were let off and bottles and barriers were thrown about.
Superintendent Caroline Hemingway said: “Following the events at Old Trafford and The Lowry on Sunday, May 2, a full investigation was launched to ensure all culpable parties were identified and face appropriate consequences.”
“Although we currently have one male in custody we are continuing to appeal to the public with information or video footage from the day to make contact with police.
“We are aware of multiple people having filmed the disorder so we urge anyone with footage that is of good quality to upload it the major incident portal or get in touch as a matter of urgency.”
Anyone with information or video footage is encouraged to upload it to GMP’s Major Incident Public Portal here or to call police on 0161 856 7573 quoting incident number 955 of 02/05/21.
Additional reporting by agencies