Dozens of people in paramilitary-style uniform attended Peggy O'Hara's funeral in Londonderry in July.  Her son was an INLA member who died on hunger strike.
Days before the funeral, footage of masked men firing shots in the city was posted on the internet.
The arrested man, who is 41 and from Derry, was detained in County Antrim.
He has been taken to Antrim police station for questioning.
The officer leading the investigation, Det Insp Philip Montgomery, has also issued a detailed appeal to witnesses who may have information about the "series of offences committed at the wake and subsequent funeral".
He appealed to anyone who saw people dressed in paramilitary-style uniform in the Templegrove area of Derry on 15 July, or who saw or heard shots being fired, to contact police.
He also asked for assistance in identifying anyone who was dressed in paramilitary-style uniform during Mrs O'Hara's funeral on 18 July 2015.
The cortege travelled from Templegrove to the City Cemetery via Buncrana Road, Northland Road, Bishop Street and Lone Moor Road.
Mrs O'Hara's son, Patsy, was one of 10 republican prisoners who died on hunger strike in the Maze Prison in 1981.
He was a senior member of the Irish National Liberation Army (INLA) - a republican paramilitary group believed to have been responsible for more than 120 murders from its formation in 1975 until its ceasefire in 1998.
A man has been arrested by police investigating paramilitary displays during the wake and funeral of a veteran republican six weeks ago.