In a statement, a spokesperson for Medina Food Services described the incident as “very distressing”.
Police have confirmed one man is in a serious and life-threatening condition in hospital.
A woman is woman sustained minor injuries and was taken to hospital as a precaution.
A 69-year-old man has been arrested on suspicion of causing serious injury by careless driving and remains in custody at this time.
A spokesperson for Medina Food Services said: “We are aware of an accident involving a Medina vehicle as it was departing the Isle of Wight ferry.
“This is obviously very distressing, and our thoughts are with everyone involved.
“We have already launched an internal investigation and are fully supporting the authorities in their ongoing investigations.”
Emergency services were called to Town Quay Road at 10.46am.
Red Funnel said vehicles coming from Southampton cannot travel currently.
For vehicles coming from the Island, cars and vans up to 6.5m are able to travel.
The service is also in operation for foot passengers and cyclists.