Some vehicles were tipped off the concrete overpass and others were crushed when it fell about 15m (yards) onto a road below.
Heavy lifting gear was brought in to reach people trapped in the rubble. The cause of the collapse is not yet known.
Witnesses spoke of a huge bang, which made them think an earthquake had struck or a bomb had gone off.
Crowds of onlookers were asked to move away from the collapsed structure which was hanging precariously.
Bystanders and relatives of people trapped under the rubble grew angry with the slow pace of rescue efforts and threw stones at security forces sent to the scene, according to the Associated Press news agency.
Karachi's mayor said the bridge was built by the state-run National Highway Authority and officially opened by President Pervez Musharraf last month.
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