Dr Haines, 65, was outside her electorate office in Wangaratta, in Victoria's north, when she was struck by the vehicle and sustained critical injuries, at about 3.35pm on Monday afternoon.
The independent member for Indi was airlifted to a hospital in Melbourne, where she underwent surgery overnight, but remains in critical condition.
"What witnesses have described is the driver doing a U-turn to get into the car park and to ram Helen against a vehicle, then to reverse and do it a second time," Home Affairs Minister Tony Burke told ABC Radio on Tuesday.
"A bystander ran towards the scene, got the driver out of the vehicle and held the driver until police arrived."
Prime Minister Anthony Albanese told News24 that Dr Haines was retrieving something from the boot of her car when she was hit, with eyewitnesses describing her being pinned between the two vehicles when a bystander intervened.
A 43-year-old man from the nearby town of Tarrawingee was arrested in connection with the alleged attack, which is also being investigated by counterterrorism authorities.
Victoria Police Acting Superintendent Ashley Mason said on Tuesday there was no evidence the man was previously known to law enforcement.
"There's certainly no recent intelligence that I'm aware of that put him on our radar," he told ABC News.
The man will be questioned by investigators later on Tuesday morning after he was held at Wangaratta police station overnight.
Major crimes officers had travelled from Melbourne to the northern Victorian town to examine the crime scene, Supt Mason said, adding the investigation would zero in on potential political motivation for the attack.
The incident is being investigated by Victoria Police's counterterrorism taskforce in conjunction with spy agency ASIO and the Australian Federal Police, with the prime minister saying he will be briefed later on Tuesday.
Authorities are yet to determine the suspect's motive or establish whether he is known to Dr Haines.
The attack has been labelled clearly deliberate by Mr Albanese.
"This wasn't something with a car just going off the off the road, this is something that is very clear was aimed at causing harm to Helen Haines," he said.
A knife was seized from inside the vehicle after the bystander performed a citizens' arrest.
"I think every Australian is grateful for those moments when a hero like this runs towards the most dangerous place," Mr Burke said.
Supt Mason personally thanked the civilian for coming to Dr Haines' aid.
"This would have been such a dynamic, horrific incident to be exposed to," he said on Tuesday.
"For that individual, for any other person who came to the aid of the injured female, or assisted in the detention of that male prior to police arrival, I'd just like to personally thank you."
The attack has sent shock waves across the political spectrum, prompting calls to firm up politicians security.
It's also sparked outpourings of support from all sides for an MP said to be one of parliament's most well liked and respected figures.
It comes after a string of threats and alleged attacks on politicians in the past year.
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