The victim was Eamonn Magee Jr, 22, a professional boxer who was the son of former WBU welterweight champion Eamonn Magee Sr.
He is believed to have suffered stab wounds to his upper body.
It happened at Summerhill Park in the Twinbrook area and was reported to police at about 02:40 BST on Saturday.
The 32-year-old man was arrested in the Dunmurry area and is being questioned on suspicion of murder.
Det Ch Insp John McVea said: "We are currently investigating the circumstances which led to the death of such a young man as Eamonn, who is a son, a brother, a partner and a friend.
"I would therefore appeal to anyone who saw or heard any dispute in the Summerhill Park area, or who knows anything about this murder, to contact detectives at Lisburn police station on the non-emergency number 101."
Family friends and fellow boxers have spoken of their shock and sadness over the murder as they paid tributes to the victim.
IBF super-bantamweight champion Carl Frampton tweeted: "Absolutely terrible shocking news about Eamonn Magee Jr. May he RIP."
Olympic bronze medallist Michael Conlan tweeted: "Heard terrible news today, I knew Eamon Magee Jr very well, RIP my friend! Devastated is an understatement, rest in peace mate!"
Boxing trainer John Breen, who is friend of the Magee family, told BBC Newsline said he "couldn't believe it" when the victim's father phoned him from hospital to tell him about the murder.
"Young Eamonn Magee is a very, very quiet lad, I never heard him raising his voice to anybody. I'm devastated," Mr Breen said.
Sinn Féin assembly member Jennifer McCann said: "A young man has tragically lost his life and no matter what, he's somebody's son.
"People are waking up here this morning, they're seeing the cordoned off area, they're hearing the sad news, so people are very, very shocked and very saddened by this."
A 32-year-old man has been arrested over the murder of a man on the outskirts of west Belfast.