Operator Amey said the key route would be closed until further notice
The Queensferry Crossing will remain shut until Wednesday due to severe weather, transport secretary Michael Matheson has confirmed.
Motorists travelling southbound were advised to divert via the A985 to the Kincardine Bridge and the M9, and the reverse for northbound traffic.
The bridge is expected to remain shut throughout the Tuesday morning rush-hour.
Mr Matheson said: "Engineers have been closely monitoring and studying the unique weather conditions causing this issue with a build-up of snow and ice on the Queensferry Crossing."
"We are developing our understanding of these conditions, which involve a certain consistency of snow and/or sleet, wind speed and direction, interacting with fluctuating low temperatures. This is leading to an ice formation on the bridge’s towers and cables at low temperature which has subsequently fallen from the bridge when thawed.
He continued: “Given the weather forecast for similar cold conditions, we expect this will be during the course of Wednesday (February 12) and we will provide further updates as soon as they become available. Safety of the travelling public is paramount and we will reopen the bridge as soon as it is safe to do so.
“I appreciate the frustration this closure may cause and I very much appreciate the public’s patience and co-operation at this time.”
Up to eight vehicles were damaged as a result of the ice falls, but there were not thought to have been any major injuries.
Scotrail has put extra services in place to assist with problems caused by the road bridge's closure.
Elsewhere, the Met Office has issued an amber warning for heavy snow in southern Scotland, predicting vehicles could be come stranded and rural communities "cut off".
Running from 2pm to 9pm on Tuesday, it warns of up to 10 cm of snow and winds reaching 50mph, creating blizzard conditions and drifts.
Yellow warnings for snow and ice remain in place over much of Scotland through to Wednesday.
The M74 was closed southbound on Tuesday morning due to an overturned vehicle.
Diversions were put in place at junction 11.
The extreme weather also hit rail and ferry travel.
Cross-border rail services were hit by a landslip between Kilmarnock and Dumfries, forcing the closure of the Glasgow Central to Carlisle line via Dumfries.
Trains will start from Kilmarnock until the route is safe.
The conditions also affected the West Highland Line and Airdrie to Balloch service, while buses replaced trains between Dumfries and Carlisle.
More than a dozen ferry services were cancelled on Monday due to the high winds, with others delayed or rescheduled.
On Tuesday morning, nine out of 28 services were cancelled amid poor weather, with the remainder delayed or rescheduled.
Meanwhile, four people had to be rescued from Ben Nevis in the Highlands after getting caught in "horrendous" blizzard conditions without the proper kit.