The incident occurred as the Tesla boss was driving out of the car park of a high-end restaurant, where he was dining with friends.
Celebrity news site TMZ reported that valets at the restaurant had parked the electric truck at the front of the restaurant, causing patrons and passers by to gather around and photograph it.
One of the admirers was Hollywood star Edward Norton, who came out of the restaurant to check out the unusual vehicle.
After cushing the traffic bollard with one of the armoured truck's rear wheels, Mr Musk continued driving and did not appear to stop to see if any damage had been caused.
— Janne Wolterbeek ⚡️ (@langejanne)December 8, 2019
Video of the Cybertruck running over the post is the second embarrassing incident involving Tesla's latest model since it was unveiled last month.
Two of the truck's windows were smashed with a steel ball during the launch event in a failed demonstration of how tough the glass is.
"Oh my f****** god," Mr Musk said after the first window broke. "Well, maybe that was a little too hard."
A demo of the "literally bulletproof" door panels was more successful, with the ultra-hard steel able to resist several blows from a sledgehammer without sustaining any visible damage.
The Cybertruck did not seem to be in any way damaged after crashing into the bollard.
The futuristic design was described as "stylistically breathtaking" by Blade Runner artistic director Syd Mead, however others claim it could pose a danger to other road users.
Chief executive of Australian car safety rating organisation ANCAP James Goodwin said the angular design was "fairly harsh" and didn't have "a whole lot of areas that would provide some give if there was a strike with a pedestrian".
He told Australian media: "We do both head form and leg form impacts... the [frontal area] would look like it's not very forgiving in terms of legs."