"We are aware the suspect assaulted people outside his vehicle," Detective Superintendent Paul Hurley from South Wales Police said.
The Friday afternoon incident in Cardiff caused the death of Karina Menzies, 32, a mother of three, The Daily Telegraph reported.
Nine of the 14 other people who were injured were hospitalized.
"These are traumatic events for the community to deal with. We have 70 officers working on this investigation," Hurley said. "Our priority is to unravel exactly what happened."
A 31-year-old man has been taken into custody on suspicion of murder.