Mustafa Kamal, the mayor of Karachi, said the authorities were using heavy machinery and bulldozers to remove debris and pull out injured people trapped in at least two or three vehicles.
The cause of the accident was not immediately clear.
Witnesses said a portion of the bridge known as Northern Bypass fell with a huge bang while traffic was on it.
Mohammed Iqbal, a survivor who escaped through the window of a small bus that fell from the bridge, told the Pakistani Geo news channel he had heard cries for help from those trapped in the rubble.
Zahid Khan, a witness, said "It created such a huge sound that we thought it was an earthquake."
Shaukat Aziz, the Pakistani prime minister, expressed sorrow over the loss of life and concern over the quality of construction of the bridge.
"Investigations have been ordered to find the reasons of the collapse and people responsible for substandard construction would be taken to task," Aziz said.
Later reports said bystanders and relatives of those trapped under the rubble, angered at what they believed were slow rescue efforts, threw stones at the security forces deployed at the scene, injuring two.
In response, the security forces baton-charged the crowd.