Detectives investigating shots fired in the Divis area of west Belfast on Monday May 20 arrested the man under the Terrorism Act 2000.
He was arrested in west Belfast on Tuesday morning on suspicion of membership of a proscribed organisation and is currently being questioned in the Serious Crime Suite at Musgrave Police Station.
A volley of shots were fired into the air at the wake of McElkerney who died after shooting himself in Milltown cemetery.
Detective Inspector Carol Dane appealed for anyone with information to come forward.
“The scene at Ross Street on Monday 20th May, of a man shooting an automatic weapon into the air was not only shocking and reckless, but also a criminal act, which was carried out by those who seek to control communities through fear of violence,” said DI Dane.
“The investigation into this incident is ongoing and Police continue to appeal to anyone with information to contact police on 101.
“Alternatively, information can be provided anonymously by contacting the independent charity Crimestoppers on 0800 555 111.”