The party's Infrastructure Minister, Chris Hazzard, and his colleague, John O'Dowd, are in London for a meeting with Brexit Secretary David Davis.
The DUP's Junior Minister, Alastair Ross, is also attending.
However, Sinn Féin has accused the government of treating the council as a "talking shop".
Earlier this week, Prime Minister Theresa May said Brexit means leaving the European Customs Union.
It currently allows tariff and paperwork-free trade between the UK and the Republic of Ireland.
Sinn Féin MLA John O'Dowd said on Thursday: "By making her so-called keynote speech on Brexit... this week two days ahead of the Joint Ministerial Council, British Prime Minister Theresa May treated the council with utter disdain."
He added: "That was a clear act of bad faith... it is clear she is intent on ignoring the will of the majority of people in the north who voted to remain in the EU.
"It has got to the stage where the Joint Ministerial Council is being treated as a talking shop by the British government and we will be reassessing our involvement with it."
The DUP see the council as a useful forum to air their concerns.
The DUP and Sinn Féin were joined at the council meeting by ministers from Scotland and Wales.
Northern Ireland Office minister Lord Dunlop described the talks as "a constructive session in looking at the devolved administrations' important contribution to the process of planning the UK's departure from the European Union".
"In her speech this week, the prime minister emphasised the importance of working together to achieve a deal that works for Northern Ireland as part of a United Kingdom that is determined to take advantage of the opportunities that leaving the EU presents," he said.
Earlier, Mr Hazzard said Northern Ireland needed a "special designated status" within the EU.
Former Taoiseach (Irish prime minister) John Bruton has said Mrs May's plan for a post-Brexit customs deal will be "unworkable".
Sinn Féin has said exiting the European Customs Union creates a "hard border on the island of Ireland".
But DUP MP Sammy Wilson said the prime minister's statement would give the business community "more certainty".
Brexit Secretary David Davis has said the UK leaving the EU would result in difficulties over border controls on the island of Ireland, but that any problems could be solved.
What is a customs union and why does it matter?
A customs union is a form of trade agreement between two or more countries.
It means they decide not to impose tariffs (taxes on imports) on each other's goods and agree to impose common external tariffs on goods from countries outside their customs union.
Setting common external tariffs is what distinguishes a customs union from a free trade area.
The key argument for leaving the customs union is that it will allow the UK to negotiate its own trade agreements.
Read more here.
Sinn Féin is threatening to pull out of the Joint Ministerial Council over concerns about negotiations for the UK to leave the EU.