Michael Russell said the UK Government may even grant a Section 30 order allowing the Scottish Government to stage such a vote.
“The choice will come - we just have to see how we get there,” Mr Russell told an audience at the Edinburgh Festival yesterday.
He was speaking after the former president of the European Council, Herman, Von Rompuy, warned a no-deal Brexit could lead to the break-up of the UK.
First Minister Nicola Sturgeon has previously said she will provide an update on plans for a second independence referendum in autumn, and has said leaving the UK without an agreement would be an “unmitigated disaster”.
But Mr Russell said yesterday: “I don’t accept the premise that there won’t be a Section 30 order, I think that is something which is still a possibility.
“The outcome will have to be a choice that the people of Scotland will have to make between Brexit and another future. There’s no other future but independence in those circumstances.
“When we get to the stage that it’s Brexit or independence, people will have to be asked that question.
“I don’t know when that will be – but I do not doubt that will have to happen. As to how that happens, that’s what we need to work on.”
Mr Russell added that to hold a referendum, both Westminster and Holyrood must vote to allow this to happen. The Edinburgh Agreement signed by David Cameron and Alex Salmond in 2013 to pave the way for the last referendum included a section 30 order and a timescale for the vote.
“A section 30 order gives you powers to do something that you don’t presently have,” Mr Russell added.
“My view is the choice will come – we just have to see how we get there.”
Westminster has responsibility for the constitution in the UK and Theresa May has so far ruled out the prospect of allowing a second referendum.
Mr Russell also indicated that EU leaders will back an independent Scotland’s membership in the event of a Yes vote.
In 2014, the EU said Scotland would be out of the Brussels bloc and forced to re-apply – a process that could take years.
“I do think that if this process is undertaken constitutionally and correctly then it will be accepted by all member states.
“But it has to be done constitutionally and correctly, and that’s what we will do. We’re not going to put ourselves outside the law, because that would be counterproductive.
“I do detect throughout the EU a much stronger sympathy. I do think that the scepticism of 2014 has gone away.”