Biden told reporters after landing near Pittsburgh early in the afternoon that he planned to go the site of the collapse.
After the snow-covered span collapsed into a ravine around 6am local time (midnight NZT), rescue workers rappelled at least 46 metres into the gully, and used ropes to help pull people to safety, Pittsburgh Fire Chief Darryl Jones said.
"They helped the fire-fighters that were here initially on scene, also did like a daisy chain, with hands just grabbing people and pulling them up," Jones said.
Ten people suffered minor injuries, including four who were taken to the hospital, city officials said. Jones added that crews planned to search under the Forbes Avenue bridge for any victims.
The collapse also caused a massive natural gas leak that forced the evacuation of several families from their homes before being brought under control, Jones said.
The US National Transportation Safety Board said it was sending a team to the site.
The incident was a high-profile example of the need to rebuild the nation's ageing bridges, highways and other infrastructure with money from a US$1 trillion (NZ$1.53 trillion) spending bill that was a signature achievement of Biden's first year in office.
Images of the collapse showed the span buckled into three large sections, with several vehicles piled in the rubble of the collapsed roadway at the bottom of the ravine. The tail end of a long, red city bus appeared trapped by the rubble.
Pennsylvania has 3,198 bridges rated as being in poor condition, according to the US Department of Transportation.
The collapse came just two weeks after Pennsylvania got US$327 million (NZ$500m) from the US Department of Transportation for bridge repair as part of the Biden administration's new infrastructure law. Pennsylvania's share of the bridge-repair money is the third largest state allocation, behind only California and New York.