Assistant Chief Constable Jenny Sims of Merseyside Police said the patients were all stable on Tuesday afternoon (early Wednesday AEST).
The 53-year-old car driver was arrested on suspicion of attempted murder, police said.
Detective Chief Superintendent Karen Jaundrill said the man was also being held on suspicion of dangerous driving and driving on drugs.
Police said the driver followed an ambulance to get through road blocks that had been set up during Liverpool’s championship parade.
