Police, paramedics and air ambulance crews were called to Bromley Road in Bellingham after the car smashed into pedestrians before slamming into a wall.
Cops said the vehicle had hit a number of people near the bus garage in Catford.
One witness reported someone trapped underneath the car.
Of the victims, a 25-year-old man remains in a critical condition.
A man, also 25, and a woman, 35, are now serious but stable.
Two other men, aged 36 and 46, are in a stable condition. Their injuries are not believed to be life-threatening.
All five victims are thought to be car wash workers.
The driver was detained at the scene and has now been arrested on suspicion of drink driving.
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Witness Minasu Towolawi ,26, told the Evening Standard: "We were on our way to church when we heard these screams.
"There's usually quite a lot of fighting round here so I just thought it was that but then my mum said, 'that's not that kind of scream..."
"We saw these people lying on the floor covered in blood, other people around them were screaming and crying, trying to help."
"I saw a well dressed man running down the street with some men chasing after him screaming, 'What the f*** have you done? Why have you done this?' Then the police came and arrested him.
"I don't understand how one person can do that to five people."
The Mercedes appears to have come off the road and careered through a row of bollards before hitting a low wall at the end of a hedge.
The car's bonnet and boot were popped open by the impact and its airbags all deployed. Debris was left strewn across the pavement.
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A spokesman said there was no suggestion the car was driven into crowds intentionally or that the incident is terror-related.
Witness, Colin Liddell, 29, added: "He turned around and sped towards the wall and hit a bollard and five people before smashing into a wall.
"At the time we thought they were all dead.
"The one that was in the car then ran away."
The crash comes after horror in New Orleans when a pick-up truck hit the Mardi Gras crowd.
Yesterday, several were injured when a car smashed into a crowd in Heidelberg, Germany.
The world has been on high alert after a string of terror attacks using vehicles as weapons hitting cities such as Nice, Berlin and Jerusalem.
A Met Police spokesman said: “Police were called at approximately 8.20am on Sunday, 26 February, to reports of a car in collision with a wall and a number of pedestrians on Bromley Road in Bellingham.
"Officers, the London Ambulance Service and London's Air Ambulance are in attendance.
“Five people were treated at the scene. They have all been taken to south and east London hospitals.
"We await an update on their condition.”
A London Ambulance Service spokesman added: “We were called at 8.18am today to reports of a road traffic collision on Bromley Road, Catford.
“We sent four ambulance crews, an air ambulance crew, a fast responder in a car, an advanced paramedic and an incident response officer to the scene, with the first of our medics arriving in under seven minutes.
“We treated five patients for a range of head, chest and leg injuries at the scene and took all five to hospital as a priority.”