Two were seriously hurt in the accident at Walton, just over the border from the Herefordshire town of Kington, at 17:30 GMT on Wednesday.
The road was closed in both directions, Mid and West Wales Fire and Rescue Service said.
Authorities have since confirmed the road reopened in the early hours of Thursday.
Three ambulances and a doctor were called to the incident and the casualties were taken to hospital.
A woman with serious injuries was described as critically ill, with a man having to be cut free from the wreckage.
A second man was described as walking wounded.
The A44 in Powys has reopened after three people were injured in a head-on collision involving two cars.