The shooting happened on Cavendish Street at about 7.45 pm on Saturday night.
The victim, who is 29, was shot in both knees and his right ankle.
He was taken to Royal Victoria Hospital for treatment to his injuries.
Sinn Féin councillor Ciaran Beattie said the attack happened in a residential area and people had been left shocked.
“I condemn these type of shootings outright – there’s no place for these actions in our society at all,” he said.
“The people responsible need to end these actions immediately and cease what they’re doing.
“It’s not wanted by the community – these attacks aren’t acceptable at all.”