Up to 12 people were trapped inside their vehicles when they plunged into the Arkansas River following the collision.
The divers are struggling against strong currents to try to find other victims.
They discovered the three bodies when they pulled a car, a pickup truck and a motor home from the water. A horse trailer with three dead horses inside was also recovered.
The accident occurred during a thunderstorm when the river was in flood, but the Governor of Oklahoma, Frank Keating, said the tug master may have had a seizure.
Engineers say it may take six months to repair the bridge, which is part of the Interstate 40, a vital east-west link. Cranes have been brought in to stabilise the remaining sections of the bridge.
The collision occurred on Sunday in a section of the river near Webbers Falls, about 100 miles (160 kilometres) east of Oklahoma City.
Click here for a map of the location
The two empty barges were being pushed up the river by a tugboat, when its master lost control and steered them into one of the supporting piers of the bridge.
Governor Keating said the tug master, named as Joe Dedmon, appeared
to have suffered a seizure and blacked out at the vessel's controls
before the collision.
Mr Dedmon is being treated at a local hospital.
Previous bridge disasters
Chad Wetz of Muscogee Medical Center, where the injured were taken, spoke to one of the survivors.
"He said he was driving along, and the next thing he
knows, there was no pavement under him, and that he was
headed for a concrete pillar of some sort and hit the water," said Mr Wetz.
The BBC's John Leyne says thousands of vehicles use the road bridge every day.
If the accident had not happened so early on a Sunday morning, he adds, many more lives would have been lost.
In September 2001, a tug boat and barge struck the Queen
Isabella Causeway in Port Isabel, Texas, causing a section of
the bridge to tumble into the bay below. Eight people died after motorists drove into the hole.
In May 1980, a freighter sheared a bridge support in Florida's
Tampa Bay, dropping a section of concrete roadway during
morning rush hour. Seven vehicles, including a bus with 26 aboard,
fell into the water, killing 35 people.
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