Queensferry Crossing: Michael Matheson 'very much regrets' bridge closure
The £1.35 billion bridge over the Forth looks likely to stay shut to traffic until Wednesday while engineers investigate the falling ice, which has affected the crossing for consecutive winters.
Speaking on the BBC's Good Morning Scotland, Mr Matheson said the bridge's designers were planning on installing ice sensors on to the structure "in the coming months" but no contract had yet been awarded for the work to be done.
Since the bridge's closure on Monday night over safety concerns, motorists are crossing the Forth via the Kincardine Bridge - a 35-mile diversion.
Mr Matheson, who said he "very much regrets" the disruption, added: "Clearly this ice build-up issue needs to be further investigated.
"There was an incident towards the end of January or February last year which was being investigated and looked at by the engineers and designers of the bridge to try to identify where the build up of ice had been taking place - whether it was on the cables or on the tower.
"As a result of that work, they've been taking forward a proposal to introduce ice sensors on to some parts of the structure.
"That work is now at a fairly advanced stage of the procurement exercise and they are due to look at the installation of the ice sensors in the coming months.
"That's to assist them in recognising that when there is a build-up of ice on any key parts of the structure that could present a safety risk, they can take action at an earlier stage in order to prevent any potential risk to bridge users."
Warning of ongoing problems for motorists, Mr Matheson said: "Given the weather forecast from the Met Office, they expect there to continue to be problems with the snow building up on the cables and - as a result of the safety risk that presents - the bridge won't open if that continues to be the case during the course of the day.
"However, should the situation change and they believe it is safe for the bridge to open again, they will do so as quickly as possible."
Scottish Conservative MSP Jamie Greene said it was "a miracle that no-one was injured", describing the falling ice as a "very fundamental and serious issue".
Criticising the failure to address the problem, Mr Greene said: "After this happened last year, we had a number of meetings in the Parliament where we questioned various Government ministers on this.
"We were given reassurances that the contractors would be looking at this as part of their snagging works and they were trying to identify the source of the problem and it would be resolved.
"It was also said that this was an unanticipated problem, so they never expected the bridge to react in this way to cold weather.
"This is a £1.3 billion bridge that was supposed to improve resilience and reliability over the Forth and motorists will be scratching their heads as to why they're going on a 30-odd-mile journey round the Kincardine Bridge when this bridge should be open and should be doing its job."
He added: "We raised this with the Scottish Government, we asked questions of the Transport Minister and frankly we were given reassurances this would be identified and resolved.
"So it's not a case of whether or not the bridge should have been closed for safety reasons, the question is why they didn't fix the problem first time round?"