The road has been closed following the crash that happened shortly after 20:00 GMT on Monday.
Witnesses said a car drove through lights and struck other vehicles then careered along the road on its roof.
Wreckage was strewn across the Falls Road between Broadway and the Royal Victoria Hospital.
The child has since been discharged from hospital. The three adults are believed to have non-life threatening injuries.
Joe Murray was waiting for a bus when the crash happened.
"I head a bang and saw a grey car hurtling towards me. I realised it had hit a couple of other cars," he said.
"My first reaction was to jump on the railings because it came that fast towards me I thought I was dead.
"I could see other people staggering about, dazed. I don't know how anybody walked out of that, all that mess."
Another witness, Daniel Murray, was sitting in his parked car with his young son at the time.
"The car came right through the lights, clipped my car, went right up, over the BMW, hit the Volvo and slid right along the road," he said.
"It was sort of like on fire and there were three boys got out and they ran away."
He said it had "scared the life out of" his son.
Four people, including a child, were taken to hospital after a crash involving five cars on the Falls Road in west Belfast.