The policy is set by the Scottish Labour Party and outlined in our last manifesto.
"Our view is that another independence referendum is irrelevant, we've got to concentrate on the real issues facing people and yes, there will be a debate about the attitude of the UK Parliament and I've made my view clear on that", he said.
Scottish Labour leader Richard Leonard said he spoke to the shadow chancellor on Wednesday morning to outline his position on the issue.
He said: "What I said yesterday, that was not picked up, is actually what I want is a Labour government, and let us demonstrate as a Labour Government what we can do to transform people's lives, and if, after a few years, people come back and say they want to test the water on an independence referendum then fair enough, that's up to the Scottish people and the Scottish Parliament".
Mr McDonnell's view contradicts that of Scottish Labour leader Richard Leonard.
No meeting of the Scottish Parliamentary Party took place before the statement was issued.
Scottish Labour leader Richard Leonard.
Another source said Mr Leonard's internal opponents were acting as "wolves in sheep's clothing" and were "attempting to stoke division".
"The 2014 referendum was a once-in-a-generation vote", he said.
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Nicola Sturgeon has said Labour is the "stumbling block" to forming a progressive alliance to halt the Conservatives. Labour will tell the Queen, "We're taking over", he said. It turns Labour Party policy in Scotland on its head.
And seizing on the comments, the Scottish Conservative leader Ruth Davidson said Mr McDonnell's remarks were met with "complete dismay" by Labour voters in Scotland. For Labour members that's what we want to campaign on and we don't want to be sidelined by another referendum, that's why we argue against it.
"The Labour Party is an internationalist party founded on a vision of solidarity and we should never seek to appease nationalists, whether they be for Brexit or Scottish independence, who want to divide communities and people".
The shadow chancellor made the comments at a Fringe event in Edinburgh on Tuesday and he reiterated his position at another event the following day. But when it comes to countries breaking free, Brexit might just be the start. Boris Johnson is getting organised and is careering towards a damaging Brexit so time is short.
"It's clear only the Liberal Democrats are robustly standing up for Scotland's place in the United Kingdom and the European Union".
Leonard told the BBC in March that if Labour took power in Westminster, the party would refuse to grant a Section 30 order - a mechanism giving Holyrood the power to hold another vote.
But the most significant intervention of the day came in Scotland.
"They're more interested in siding with the Tories and fighting with each other than defending Scotland's interests".
"People in Scotland should be able to make a fundamental decision about do you want to crash out of the European Union for a no-deal Brexit or make our own decisions like our neighbours in Ireland and Denmark".