The car, a grey coloured Hyundai i40 taxi, was hijacked by two men armed with a baton and a suspected firearm at around 6.05pm.
The taxi was abandoned minutes later, a short distance away in Ladymar Walk after encountering a passing police patrol.
The two males made off from the area on foot and the taxi driver reported an injury to his shoulder from being struck with the baton.
Investigating officer Detective Constable Gareth Hussey said, “ We are seeking information about this incident and an incident which occurred in Northumberland Street at around 5.50pm when two men matching the descriptions of the hijackers were reported to have attacked a passing car with a baton and a firearm.
“Both were described as being around 30 years old and were wearing dark clothing with hooded tops.
“No damage was caused to the car and there were no injuries reported. The men made off in the direction of the Falls Road.
“I would appeal to anyone who witnessed either incident or who has any information which may assist us with our enquiries to contact CID in Tennent Street on 101.
“Information can also be passed anonymously through the independent charity Crimestoppers on 0800 555 111.”