The 71km pursuit lasted about 50 minutes.
Northland road policing manager Inspector Wayne Ewers said search and rescue are carrying out a sweep of the riverbank and police are searching surrounding areas.
The identity of the driver is unknown.
"We are now asking the male and female passengers of the vehicle to come forward to assist police to identify the driver.
"We have serious concerns for his safety, given the conditions of the river last night," said Mr Ewers.
A Northern Advocate reporter who was at the scene said the river was flowing swiftly and was quite swollen.
Police are asking anyone who may have been in the Central Ave and Western Hills Drive area between 6.30pm and 7.30pm to contact the police.
"We also ask that anyone living in the Parakao area who may have had someone show up unexpectedly to their home, or seen a male in the area to please call us immediately," said Mr Ewers.
Call Whangarei police on 09 430 4500 or contact Crimestoppers anonymously on 0800 555 111.
