SDLP West Belfast MLA Alex Attwood condemned the shooting.
"I condemn this latest act of tyranny in west Belfast. The fact that two people, a man and a woman and both in their fifties, have been injured confirms that no one is off limits to those who are now using the gun," he said.
"I have spoken with senior police tonight. They are looking for the help of the public. The public must give the police help."
Detective Sergeant Keith Wilson said: "Both the man and the woman have been taken to hospital for treatment to their injuries.
"I would ask anyone with any information about this incident, or anyone who noticed any suspicious activity in the area, to contact detectives at Musgrave Police Station on the non-emergency number 101, quoting reference number 900 of 12/01/17.
"Or if someone would prefer to provide information without giving their details, they can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111."