Dr Haines, 65, is in a critical condition after being hit by a vehicle while loading up her car on the main street of Wangaratta, in Victoria's north, on Monday afternoon.
She is being airlifted to a hospital in Melbourne for further medical treatment.
The 43-year-old male driver, from the nearby town of Tarrawingee, is in custody after a bystander performed a citizen's arrest.
A knife was seized from inside the suspect's Toyota Landcruiser, police said.
Authorities are yet to determine the motive for the attack or establish whether the two parties are known to each other.
The national joint counter-terrorism team, including representatives from the Australian Federal Police and spy agency ASIO, had begun investigations alongside state authorities, Prime Minister Anthony Albanese said.
There was "no place for political violence" in Australia, Mr Albanese said.
"This wasn't an accident. There was a deliberate act, it would appear," he told the ABC's 7.30 program.
"We don't know what the motivation is. So that is the work that's being undertaken."
The prime minister said he was not aware of any personal threats being made against Dr Haines.
"Helen Haines is incredibly hardworking. She is fiercely intelligent, but most importantly, she's just a thoroughly decent human being, full of integrity, and respected right across the parliament," Mr Albanese said.
Victoria Police Acting Superintendent Ashley Mason thanked members of the community who had stepped in to help.
"This would have been a tragic, horrific incident for people to witness," Act Supt Mason said.
"But I just thank those that were nearby and those that were involved and assisted in detaining the male, and then also provided any assistance to the injured female."
The attack has been condemned by MPs and senators from across the political spectrum.
It was a shocking day for the nation, Opposition Leader Angus Taylor said.
"No one should be targeted in this way," he said in a statement.
"Our nation cannot become a place where violent attacks are normalised."
Zali Steggall, who sits next to Dr Haines in the House of Representatives, said she was shocked and devastated.
"I have worked with Helen since 2019 ... she is a wonderful, caring, smart and wise friend and amazing representative for her community," she said in a statement.
"I am thinking of Helen and her wonderful family."
Threats and incidents against federal parliamentarians had increased year on year, Home Affairs Minister Tony Burke said.
"The year before last, we had 951 reports of harassing and threatening behaviour against various high office holders," Mr Burke told reporters in Sydney.
"The more recent financial year, that 951 has gone to 1067."
Dr Haines represented the best of the nation, crossbench colleague and frequent collaborator David Pocock said.
"Helen represents so much of the values we share as Australians," Senator Pocock said in a post to social media.
"At a moment like this we should turn to them more than ever and be sure to take care of one another."
Greens leader David Shoebridge, One Nation leader Pauline Hanson, Victorian Premier Ben Carroll and state Liberal counterpart Jess Wilson were among many others wishing Dr Haines a full recovery.
Dr Haines has represented the regional seat of Indi as an independent since 2019, coming to prominence on her platform of political transparency and integrity.
Her family thanked bystanders and emergency workers who had assisted "our beloved Helen".
"Please keep Helen in your thoughts," they said in a statement.
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