Alex Neil says the best date for a second independence referendum would be after the 2020 general election.
Despite his remarks, an SNP spokesman said: “People across Scotland should have the ability to consider the question of independence - and to do so before the UK leaves the EU - if it becomes clear it is the best or only way to protect our country’s interests.”
Mr Neil however believes this may be too soon.
“You cannot realistically maximize your chances of winning a referendum for independence unless and until you know what the final Brexit deal is,” he said.
“The reality is that after the statement by Michel Barnier (EU chief negotiator) that the deal has got to be done in the next 18 months, physically it would be very difficult to get an independence referendum in that time.
“Realistically any referendum on independence is going to come after the deal is done.”
Mr Neil. who stood down as justice sectary in May, said the best time for indyref2 would be after the next general election.
“Let’s not have a premature referendum which we might not win because we don’t have all the answers,” he added.
Though First Minister Nicola Sturgeon has never committed herself to a date for a second referendum on Scottish independence, she told delegates at October’s SNP conference she would like to see it happen before the UK leaves the EU.