Hwyel Dda health board said its teams were responding to the incident.
“Our emergency departments are busy, and waiting times are likely to be longer as we treat individuals with the greatest need first,” it said.
Local vicar Father Jim Flanagan said he was re-routed due to the road closures and saw the roof of a bus over a hedge.
He added there were multiple ambulances there, with lights flashing, and an air ambulance had landed in a field.
One of his churches, St Mary’s in Kidwelly, has been opened should people wish to use it, he said.
