The van crashed through the bridge's barrier and into the water in the collision. The two other vehicles remained facing towards Te Maunga on the bridge.
Glass and bits of metal were thrown over a large area.
A Tauranga St John spokesman said it appeared a car travelling south-bound toward Te Maunga drove head-on into another car heading toward Maungatapu.
The impact caused one car to ricochet into the eastern side of the bridge, he said.
An off-duty police officer, who lives in Maungatapu, aided search efforts by using his canoe to try to help find the missing driver.
He spent about 40 minutes searching the incoming tide. The wind was especially strong under the bridge, he said.
Welcome Bay resident Josh Howard said he heard sirens and about 10 minutes later saw the lights on the bridge from his home "so I just came on over".
"I was definitely worried it might have been someone I know."
Maungatapu resident Hannah Handforth was among a small crowd of concerned residents who gathered at the shores of Maungatapu Marae.
The Trustpower Tect Rescue Helicopter and Coastguard boat could be seen searching the waters near the bridge as more people gathered.
Ms Handforth said news of the crash was quickly posted on Facebook and she assumed it would have been from teenagers on buses she saw caught in the traffic.
Acting Senior Sergeant Wayne Hunter said the driver's identity was yet to be established.
When the Bay of Plenty Times went to print last night, the police officer who rescued the passenger was expected to be discharged from hospital, possibly along with the 23-year-old man he saved.
A 30-year-old woman and 31-year-old man who were in the same car were also treated at hospital. The woman was expected to be discharged but the man was likely to be kept overnight.
A 45-year-old man travelling in another car remained in the emergency department.
Another Maungatapu resident said traffic was backed up for kilometres in both directions for about an hour.
It was not the first time a car had gone off the bridge, she said. "There's so many accidents on that bridge, I don't know why.
"Whether people are looking away at Tauranga in the distance, or something going on in the water, I don't know."
In January 2010, a 60-year-old Tauranga woman died in the wreckage of her SUV from a head-on crash on Maungatapu Bridge with a ute driven by a 17-year-old youth.
He received serious neck and abdominal injuries.