The 53-year-old is described as white British and from the West Derby area of Liverpool.
Police say 11 people who were still being treated in hospital are recovering well. A total of 65 people were injured, they said.
Liverpool parade latest: Follow updates after man’s arrest
At a press briefing this afternoon, assistant chief constable Jenny Sims said the car followed an ambulance after a road block on Water Street was lifted so paramedics could help a man who had a suspected heart attack.
The car entered the road from Rumford Street, Merseyside Police said.
Detectives have said the incident is not being treated as terror-related, and no further suspects are being sought.
“There was no intelligence to suggest an incident of this nature would take place,” Ms Sims said.
She also defended the policing operation during the parade, saying the force planned for “all contingencies”.
Her comment came after the city’s metro mayor Steve Rotheram said questions about how the car was able to enter the road were “legitimate”.
The arrested man remains in custody and is being interviewed by officers, police said.
Merseyside Police is receiving help from neighbouring forces “due to the number of victims”, detective chief superintendent Karen Jaundrill added.
She continued: “Extensive CCTV inquiries are being carried out across the city to establish the movements of the car, a Ford Galaxy, before the incident took place.
“We have already had an incredible response from many of those who were there last night.”
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Messages of support have been sent to the people of Liverpool since the incident, with the Prince and Princess of Wales saying they were “deeply saddened” by the events.
“What should have been a joyful celebration ended with tragedy,” they added.
