David Mundell’s comments come as pressure mounts on Nicola Sturgeon to outline her position on a further referendum as senior SNP figures called for the vote to be postponed.
Ms Sturgeon said independence was a factor after her party lost 21 seats in the General Election, and vowed to “reflect on the result”.
Mr Mundell told the BBC’s Sunday Politics Scotland: “The people of Scotland sent Nicola Sturgeon and the SNP a very, very clear message in last week’s General Election - with the cataclysmic performance of the SNP compared to the 2015 general election. They want that threat of an independence referendum taken off the table.
“Nicola Sturgeon should not be in denial about that. She should wake up, smell the coffee and be absolutely clear with the people of Scotland, as now members of her own party are indicating, and take that threat off the table.
“I don’t see any circumstances in which there is going to be an independence referendum before the 2021 Scottish Parliament elections.”
Deputy First Minister John Swinney told the same programme: “Our proposal always was that we should have this referendum, if we have it, at the end of the Brexit process. We’ll consider those proposals and we will consider them in the light of the election campaign.”
He said the end of the Brexit process would be at the end of March 2019, two years after the triggering of Article 50.
SNP MP Tommy Sheppard said the independence campaign should be “parked” until Brexit negotiations are over.
He wrote in the Sunday Herald: “Amidst the current chaos in Westminster it seems certain that a hard Brexit is now off the table, and the possibility of bespoke solutions for nations and regions is growing.
“It follows, therefore, that it is now an option to wait until the Brexit negotiations conclude before forming a view on whether the extent of change justifies a second independence referendum as a result. This would mean that whilst a second referendum remains an option, the timetable gets parked.”
Meanwhile, former SNP political adviser Alex Bell said the party should “shut up about indyref2”, adding “the UK is in genuine crisis and there’s no loss of face in letting that settle until some undetermined date”.
Former justice secretary Kenny MacAskill said the SNP should “abandon” its current referendum push as “neither the mood is there for it, nor the support in existence to win it”.
Scottish Labour election campaign manager James Kelly said calls for Ms Sturgeon to ditch plans for a second referendum are now “deafening”.
He said: “The uncomfortable truth for the SNP leader is that Scots don’t want another referendum - they want her to get on with the job of fixing the mess she has made of our schools and hospitals.
“Now even senior figures in her own party seem to agree.”