A portion of the concrete overpass gave way when a heavy trawler crossed it after 1pm, tipping vehicles off and falling about 15m onto the road below.
The 57km-long Northern Bypass opened just one month ago by Pakistan president Pervez Musharraf.
The cause of the collapse is unknown but a government inquiry has been ordered.
Federal communications minister Shamim Siddique told the Hindustan Times: "The inquiry will find out why the Baldia loop of the bypass collapsed and if necessary I am also willing to submit my resignation as this is a national tragedy and should have been avoided."
He added that he had earlier pointed out structural flaws in a portion of the bypass, which was built by the state owned National Logistic Cell (NLC).
A regional governor visited the site on Sunday, announcing that experts would also inspect the city’s other bridges and flyovers. However he is reported to rule out closing these bridges to traffic.
Rescue workers are using heavy lifting equipment to search the rubble but officials have no idea how many more people are stuck in the debris.