Mike Russell said he only found out the process would formally get under way on March 29 when it was reported by the BBC.
Russell, the minister for UK negotiations on Scotland's place in Europe, has been involved in discussions between London and Edinburgh over the Article 50 process as a member of the Joint Ministerial Committee (EU Negotiations).
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He claimed he had not been informed by Downing Street about the Prime Minister's intended date for triggering Article 50.
Theresa May's letter officially notifying the European Council of the UK's intention to quit will set in motion a two-year negotiation process expected to lead to Britain leaving the EU on March 29 2019.
Britain's ambassador to the EU, Sir Tim Barrow, informed the office of European Council president Donald Tusk on Monday morning of the Prime Minister's plans.
Russell tweeted: "Thank you @BBCNews for letting JMC members like me know that #Article50 is to be triggered next week. @GOVUK somehow forgot to inform us."
Martin Docherty, MP for West Dunbartonshire, said on Twitter: "In the entire process this is extraordinary #Brexit chaos #Article50."
Colleague Roger Mullin, who represents Kirkcaldy and Cowdenbeath, tweeted: "Outrageous but typical of UK government arrogance and complete dismissal of Scottish interests. #indyref2."
The row comes amid increasing tension between Edinburgh and London over Brexit after Scottish First Minister Nicola Sturgeon announced plans to seek to hold a second independence referendum in the wake of the vote to quit the European Union.
While the UK as whole backed the UK's departure, 62% of voters north of the border wanted to remain.
SNP ministers insist the result gives them a "cast-iron mandate" to stage a second independence referendum after the party's manifesto for the 2016 Holyrood elections said such a vote should be held if there was a "material change in circumstances" from the 2014 ballot, citing the example of Scotland being removed from the EU against its wishes.
MSPs are expected to back Sturgeon's call for a fresh referendum to be held in a vote at Holyrood on Wednesday - which will then see the Scottish Government formally request a Section 30 order from Westminster, enabling a legally binding vote to take place.
However, May has already said "now is not the time" for another ballot on the future of the UK to be held.
The Prime Minister said she had discussed the Article 50 notification with Welsh First Minister Carwyn Jones during a visit to Swansea this morning.
"I have had an opportunity to talk to Carwyn today about the process we will be going through in terms of the triggering of Article 50 leading to the negotiations," she said.
"We have been talking with the Welsh Government for the past few months and with the other devolved administrations about the process, about the timetable.
"I have always said it would be before the end of March and we will continue talking to them."