The closure of the Forth Road Bridge until the new year is a matter of "national significance", Scottish Transport Minister Derek Mackay has said.
He called for understanding from the public across Scotland as repair work is carried out on a structural fault on the crossing.
The decision to close the bridge was taken by the Scottish Government after inspections carried out by specialist engineers and following advice and assessment of the fault by independent experts.
The complete closure came into force at midnight, with major tailbacks experienced on diversion routes at rush hour on Friday morning.
Mr Mackay said the decision was "not taken lightly", and steps are being taken to lessen the impact of the closure.
The problem was first identified during a routine inspection on Tuesday. Traffic was restricted that evening but it was later decided that the bridge should be closed entirely.
Additional rail, ferry and park-and-ride facilities are to be put in place. Emergency service vehicles will still be able to use the bridge when responding to calls.
Engineers said a 20mm crack in a truss under the southbound carriageway close to the bridge's north tower could not have been predicted and happened quickly.
The area had been inspected in May and no damage was found, but a routine inspection of another element had brought the fault to engineers' attention.
They said that continuing to allow traffic to use the bridge would "increase the risk of causing extensive secondary damage to the structure".
It is anticipated it will take around a week for design, further inspections and preparatory work to be undertaken, followed by around two weeks to carry out the repair work.
Timescales could be affected by adverse weather conditions.
Mr Mackay said: "Every effort is being made to open the bridge as quickly as possible but safety is the main priority, however these works are weather dependent given the height and location of the bridge.
"We are aware of the potential economic impact, for strategic traffic in the east of Scotland and on people living in local communities.
"This is an unprecedented challenge in the maintenance of the Forth Road Bridge. On balance following advice from engineers and independent experts, the full closure is essential for the safety of the travelling public and to prevent further damage to the structure of the bridge.
"The bridge operators Amey have a robust inspection team in place and these defects are problems that have only occurred in the last number of weeks.
"We are taking every step we can to lessen the impact of this closure. Action now will mean that any closure is much shorter than it might be if we waited."
He added: "I am sure the population of the whole country will recognise that this isn't just a local matter. This is a matter of national significance."
Mr Mackay said every effort is being made to identify available rolling stock for the rail network, while people are also being encouraged to car share, travel outside peak times and agree flexible working solutions with their employers where possible.
The closure could have a knock-on impact on rail services across the rest of the country.
ScotRail said it is adding extra carriages and staff for services on the rail bridge to and from Fife, saying it is a "national priority".
Mr Mackay said: "We want to identify any available rolling stock from elsewhere. The current rolling stock in Scotland is used at maximum capacity.
"If some of it (the rolling stock) comes from another area, there has to be a degree of understanding about the support provided in view of the decision taken to close the bridge."
On the economic impact, he added: "We will engage with the business community and if there are any other measures we can take, we are all ears."
Chartered engineer Mark Arndt, from Amey, said: "This is a complex engineering challenge. The component failure is in a difficult-to-access location and our response is also highly dependent on weather conditions.
"We continue to work around the clock on inspections, assessments and calculations along with the development of designs to effect the necessary repairs, while at the same time mobilising all the resources required to reopen the bridge as soon as is possible."
Engineers said further damage to the section could have caused the bridge deck to drop by around six inches and would have led to the closure of the crossing for "a number of months".
About 70,000 vehicles cross the bridge each week day, and around 24 million every year.
Long delays were reported on alternative routes during Friday morning's rush-hour, with Traffic Scotland warning of tailbacks stretching to 11 miles at one point on the approach to the Kincardine bridge, while there was a six-mile queue around the Clackmannanshire bridge.