Eamonn Magee Jr, aged 22, was stabbed in the Twinbrook area of West Belfast during the early hours of Saturday morning and died in hospital from his injuries.
His father is former WBU welterweight champion Eamonn Magee Sr. The suspect, aged 32, was arrested in the nearby Dunmurry area.
Mr Magee Jr had followed his father into the ring and his death has sent shockwaves through the world of boxing.
IBF super-bantamweight champion Carl Frampton used Twitter to say: “Absolutely terrible shocking news about Eamonn Magee Jr. May he RIP.”
Sinn Féin MLA Jennifer McCann said the community in West Belfast had been stunned by the brutal killing.
“A young man has tragically lost his life and no matter what, he’s somebody’s son,” said Ms MCCann. “This is an absolute tragedy for his family and the local community are in shock. I extend my condolences to the family of the victim and I appeal to local people to assist the police in any way they can in their investigation.”
Mr Magee Sr was known as the Terminator during his professional career, and enjoyed Commonwealth success. Among his most high profile fights was the 2002 sell-out bout against ex-world champion Ricky Hatton in Manchester.
Since retiring he hasworked as a trainer at Breen’s Gym in Belfast.
Last year he was convicted of a drunken assault on his wife, but avoided jail when his sentence was suspended.
Detectives have urged anyone with information on the death to come forward.