An investigation has been launched into the incident, which the Scottish Government’s Transport Scotland agency confirmed happened on Saturday, 16 March.
Officials are also exploring possible preventive measures, which The Scotsman understands could include remotely-operated devices to clear ice from the cables.
Transport Scotland said the hazard was considered in the bridge design process, but such incidents were rare.
It is understood traffic has had to be stopped only once to clear ice from the cables on the adjacent Forth Road Bridge since it was opened 54 years ago.
Transport Scotland said such ice build-ups had not been a problem on other major Scottish crossings, such as the Kessock Bridge in Inverness, which is of a similar cable-stayed design.
However, both road bridges over the Severn in south-west England had to be closed ten years ago after ice fell from gantries on the Second Severn Crossing.
Transport Scotland said the Queensferry Crossing would be monitored during icy weather by the Forth Crossing Bridge Constructors (FCBC) group, which is still completing work on the 18-month-old structure.
It said the group would liaise with road maintenance firm Amey over any necessary traffic restrictions, which it is understood could include lane, carriageway or a complete bridge closure.
A Transport Scotland spokesman said: “We are aware of three reports of damage seemingly caused by falling ice on 16 March. These incidents are being looked into.
“We are aware this is an issue that, in certain weather conditions, has occasionally affected other structures across the UK.
“In previous years, the Forth Road Bridge was briefly closed to traffic to allow for ice to be cleared from the cables, without any significant traffic impact.
“FCBC will be monitoring the Queensferry Crossing during icy conditions and will liaise with Amey to manage traffic, if required, to ensure public safety.”
The spokesman said this would be dealt with in a similar way to other hazards, such as crashes, breakdowns or spillages on the road.
He added: “We continue to explore other methods and innovations to prevent this from happening in future.”
The spokesman said details “will follow the investigation into what happened and how it was caused”.
The crossing is a key part of Scotland’s road network, carrying more than 70,000 vehicles a day between Fife and Edinburgh.
Transport Scotland said wind shielding had enabled the bridge to stay open during high winds when the Forth Road Bridge would be closed.