The man was airlifted to a major trauma centre and the woman was also taken to hospital after the incident at the Dunelm car park on Sunday.
The van is understood to have crashed into the two pedestrians and a wall at the shop off the A41 Bilston Road just before 2.30pm.
Paramedics and police were called and the helicopter landed on the nearby Carpetright car park.
West Midlands Police said the man and woman both suffered broken legs and that the van driver is now assisting officers with their investigation.
Photos from the scene showed some of the medics covered in paint after treating the victims.
Two bystanders were also treated but did not need hospital treatment.
A West Midlands Ambulance Service spokesman said: “On arrival, ambulance crews found the man and woman at the base of a collapsed wall beside a van.
“The man had suffered serious injuries and after assessment at the scene, was airlifted to the major trauma centre at Queen Elizabeth Hospital Birmingham.
“The woman who was with him was also assessed and treated at the scene before being taken to New Cross Hospital by ambulance.
“Two other people who witnessed what happened were also assessed but were discharged at the scene.”
Anyone with information is asked to contact police online or by calling 101 quoting 2269 of October 25. Alternatively Crimestoppers can be called anonymously on 0800 555 111.