The A40 between Nantgaredig and Whitemill is closed and diversions are in place following the incident at about 18:15 GMT on Friday.
A grey Smart Fortwo Prime, a black Volkswagon Golf and a grey Volvo were involved in the crash.
Dyfed Powys Police are appealing for witnesses.
Four people have been taken to hospital after a three car collision in Carmarthenshire.