A 49-year-old Girrawheen man has been remanded in custody after allegedly running down a cyclist with his four-wheel drive following an altercation in Perth's north-east.

It is alleged Jason Peter William Reah chased 18-year-old Hashem Mohamed through the car park of a Girrawheen shopping centre before running him over.

The Noranda teenager was taken to Royal Perth Hospital with life threatening injuries and remains there in a serious condition.

The Perth Magistrates Court heard Mr Mohamed was with friends in the car park at about 7:30pm when someone in the group threw a glass bottle at Mr Reah's car.

Police cordoned off the scene of the crash with the four-wheel drive parked nearby. ( ABC News )

Police said Mr Reah then drove at the group and as Mr Mohamed cycled away he followed him up a kerb, onto a median strip and hit him from behind at speed, before driving over him.

They told the court Mr Mohamed came out from under the rear of the car before it came to a stop.

As Mr Mohamed lay bleeding on the ground it is alleged Mr Reah exited his car and told someone to call an ambulance before walking off in search for his pet dog which had run out of the car.

Police said Mr Reah then returned to the scene, with his dog, and sat in his car without giving any assistance to Mr Mohamed and waited until police arrived.

In court Mr Reah said he saw that Mr Mohamed was already receiving first aid and that he was scared he might be attacked by the 18-year-old's friends.

The 18-year-old was treated at the scene by paramedics before being taken to hospital. ( ABC News )

Police say they had been told by doctors that Mr Mohamed would have died if he had not received immediate treatment at the scene, before undergoing five blood transfusions in hospital.

Through his lawyer, Mr Reah told the magistrate he was concerned for Mr Mohamed's welfare and was sorry the incident had occurred.

He has been charged with offences including dangerous driving occasioning bodily harm and failing to stop and offer assistance.

Mr Reah is also accused of refusing a police request to provide a blood test.

Police said that Mr Reah had told them after the incident that his brakes had failed.

Mr Reah's legal representation said he denied many of the allegations against him.

The court also heard Mr Reah has mental health issues and had not been taking his medication.

The Police Minister Michelle Roberts described the incident as shocking.

"Something like that just shouldn't happen. If you're on a bicycle or a motorbike you are vulnerable as a road user but the allegations here are pretty astounding," she said.

The mangled wreckage of the injured man's bicycle was left lying on the verge after he was hit. ( ABC News )

The Deputy Police Commissioner Gary Dreibergs said he hoped the victim made a full recovery.

"It's a very serious offence, it's beyond belief that somebody would do something like that in a motor vehicle," he said.

"It's beyond belief that somebody would get so close behind a person on a bicycle that they could hit them with their vehicle and knock them off, and the consequences as we've seen are very, very, serious and they could have even been more, hopefully they won't be more serious."

Mr Reah was not required to enter a plea on Sunday and will face Perth Magistrates Court again on December 23.