NSW Police are seeking two men who are believed to have fled from the scene.
Emergency services were called to the bridge about 5.45am, and police were told the man who was driving the truck had allegedly left the scene in a vehicle, driven by a second man, before they arrived.
They were allegedly spotting travelling south on Remembrance Drive.
Police say the truck was stolen from a nearby home.
Officers wish to speak with the alleged driver. He is described as being of African appearance, aged 20-30, of medium build, wearing an orange, fluorescent long-sleeved shirt, dark blue pants and a dark cap.
He is believed to have left in a black BMW with a 'suspected paint job'.
Anyone who witnessed the truck crash or who has dashcam vision from the area at the time is urged to contact police.
Prince Street, Picton remains closed and motorists are advised to avoid the area.
Picton's Victoria Bridge remains closed after a stolen truck crashed into the barrier and pulled it from the ground.
A Camden Police Area Command spokeswoman said early inquiries had led them to believe the truck was stolen from very close to the bridge.
She said whoever was driving the vehicle fled from the scene, and there were no known injuries.
Wollondilly Council and Transport for NSW have responded to the incident.
The police spokeswoman said the truck and height barrier needed to be removed with a crane.
"It's my understanding that we're waiting for a heavier duty crane to arrive at the moment," she said.
"I've been briefed that the bridge is still structurally sound, but the [barrier] was collected by the truck and pulled out of the ground.
"The bridge, the metal archway and the truck are all interconnected at the moment.
"I imagine the bridge will be closed for quite some time."
The spokeswoman said she anticipated power would be shut off to surrounding areas for a short time to aid in the removal of the vehicle and damaged height barrier.
Wollondilly deputy mayor Michael Banasik said the incident had increased traffic in Picton.
"I first saw it on social media this morning and I thought, 'what a dumb thing to do' - stealing a vehicle and having a crash like that,'' he said.
"Its school holidays now and with Covid a lot of people are working from home so traffic isn't as bad as it would be under normal circumstances."
Cr Banasik said he hoped this incident would further demonstrate the need for a Picton Bypass.
"This is further proof that we need a Picton Bypass," he said
''I know that the former MP Jai Rowell got some funding for the RMS to do a study but we haven't seen the results of that yet.
''We have been lobbying hard for the government to do something about this for a while now.''