The collisions, involving two cars and a caravan, happened north of Felin Fach at about 12:05 BST on Saturday.
A Mid and West Fire and Rescue Service spokesman said a woman was trapped but she has been freed and taken to Morriston Hospital, Swansea, via air ambulance.
Part of the road was closed but has since reopened.
A woman has been airlifted to hospital after a crash on the A470 in Powys.