The 120-tonne beam was being lifted on Balfour Beatty’s A64 flyover replacement project in the city centre.
The section of bridge was due to be transported away to be broken up ahead of new steel beams being installed above Regent Street.
Leeds City Council said: “A concrete section of the demolished bridge was being lifted onto a specialist trailer to be disposed of and recycled away from site.
“It was safely placed onto the heavy load vehicle however there was failure of the trailer, causing the piece of bridge to shift from its resting position.
“There were no accidents or injuries as a consequence of the trailer system failing and work will continue to demolish the bridge over the coming days.”
The stricken section of bridge was broken up for safe removal and cleared from the site on Saturday.
Built in the late 1960s the Regent Street Flyover, which carries traffic over the Inner Ring Road, has reached the end of its usable life.
Balfour has already successfully completed the southern bridge section of Regent Street Flyover and the project team is now on the northern bridge which is being taken down and rebuilt.
Regents Street Flyover replacement plan