Police say the 40-year-old was detained today and has been taken to the serious crime custody suite at Musgrave PSNI station for questioning.
The victim, who is in his 30s, was attacked in Westrock Gardens at about 10.30 pm on Saturday night.
He was taken to hospital for treatment and the police investigating the shooting have appealed for information.
Det Insp Paul Wright said although the man’s injuries were not life-threatening, they were potentially life-changing.
“We received a report that a man in his 30s had been shot in both legs in an alleyway close to the Westrock Gardens/Springhill Drive area of west Belfast around 10.30pm,” he said.
“This was a brutal attack and yet another example of how criminal groups seek to control communities through fear and violence.”