Delays of up to 30 minutes are expected while the last phase of work is carried out due to diversions.
At peak times, queuing systems will be in operation at Dundas St and Hanover St with passengers using one of these two entrances depending on their destination.
During his visit Mr Mackay was shown how passengers will access the platforms and met with ScotRail staff who will be on hand to assist customers throughout the diversions.
Queen Street tunnel is being upgraded to allow faster, longer, greener trains to run between Edinburgh and Glasgow and to replace aging track through the kilometre-long structure.
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The ScotRail Alliance launched a major publicity campaign in January to ensure customers have all the information they need and passenger surveys taken this week show that 80% of regular travellers know about the closure.
Mr Mackay said: "The ScotRail Alliance are confident in their ability to deliver this major and complex piece of engineering work. Recent customer surveys demonstrate high levels of awareness amongst the general public, however customers using Queen Street station particularly during peak times are reminded to visit the ScotRail website to familiarise themselves with the temporary layout of the station.
"The closure of the Queen Street Station High Level tunnel marks a further significant milestone in our £5 billion programme of investment in Scotland’s Railways and will pave the way for the introduction of a new generation of electric trains for the central belt of Scotland."
John McBrinn, senior customer manager with ScotRail Alliance, added: "Queen Street station is open for business and trains will still be running into the city. Over the next forty-eight hours we will continue to reach as many customers as possible with our key message – plan ahead and allow more time for your journey.
"All the information that people need is available on our website. We will have extra staff in stations to answer questions and help get you to your train and have also put in place a temporary marque and canopy to protect customers from the elements."
(MH)
