Two had to be cut free from wreckage when a van crashed into the back of a taxi at traffic lights at the junction of Beechmount Avenue and Falls Road.
Other vehicles, including another taxi, were also hit in the collision.
Police said none of those hurt suffered life-threatening injuries.
Three people are understood to be in a serious condition.
Officers are appealing for witnesses to contact them at Grosvenor on 0845 600 8000.
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