Engineers are currently assessing the situation.
A Council spokesman said: “The bridge was closed last week following the failure of a steel component that connected one of the hangers to the arch. The casting that failed has been taken away for inspection and testing and the Council, constructors and designers are still awaiting the results of this.
“We are carrying out inspections of all similar components on the bridge. In the course of an inspection today, a crack was found in another similar connector on a different hanger.
"The Council has, as a precautionary measure, requested that all river traffic below the bridge be suspended until further notice.”
Although Clyde Arc is designed to allow for the removal of one support at a time for repair and maintenance without affecting its operation, it is unclear at this stage what impact a second failure would have.
At this stage, it is anticipated the Arc will now be closed for up to six months.
The Clydeport Harbour Master has confirmed that traffic is minimal on the affected stretch of the Clyde, with almost no commercial use.