The woman, aged in her 20s, was allegedly struck by a campervan in the car park of Morrisons in Blackpool Road this morning.
A 74-year-old man, from Wigan, has been arrested on suspicion of dangerous driving.
A police spokesman said: "We were called at shortly before 6.25am by the ambulance service to the report of a collision involving a woman and a campervan in the car park of Morrisons on Blackpool Road, Preston.
"The woman, in her twenties, has been taken to Royal Preston Hospital in a serious condition.
"A section of the car park has been cordoned off for officers to conduct their investigation into the cause of the collision.
"The back entrance on West View also remains closed. We apologise for any inconvenience this may cause for people.
"The driver of the campervan, a 74-year-old man from Wigan, has been arrested on suspicion of dangerous driving and remains in police custody."
Staff at Morrisons confirmed that the supermarket remains open but there is limited access to the car park.
More to follow...