The pair were due to discuss the latest security developments in Northern Ireland at a meeting in Brussels.
Northern Ireland has been without an executive since January, when the governing parties - the Democratic Unionist Party (DUP) and Sinn Féin - split in a bitter row over the handling of a botched green energy scheme.
The UK government has said it will implement a budget for the region, as the parties’ continued failure to establish an executive means public services are starting to run out of money.
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The meeting with Barnier, the European Union’s chief Brexit negotiator, takes place in between Brexit negotiation rounds.
On Monday, a UK government source said Brokenshire will emphasise the “unique” issues affecting Northern Ireland as the UK prepares to leave the EU.
The minister will also update Barnier on talks to form a Northern Ireland executive and the remaining political challenges Northern Ireland faces in relation to exiting the EU.
He will also hold meetings with Julian King, the British European Commissioner, and Phil Hogan, the Commissioner for agriculture and rural development, to discuss Northern Ireland’s agricultural interests in view of Brexit.
The source said the Secretary of State will also use the opportunity to update MEPs on various issues.
Brokenshire said, “My visit to Brussels today comes at an important time. Negotiations are underway and we want to secure an agreement that delivers for all parts of the UK, including Northern Ireland.
“As Secretary of State I am fully committed to ensuring that, as negotiations progress, the interests of Northern Ireland are protected and advanced, through the development of specific solutions to address its unique circumstances.
“Of course, it would be better if there were an executive in place, with whom we could also engage directly, and that is why we are working to ensure the resumption of stable devolved government in Northern Ireland. My department and I will continue to advocate for Northern Ireland’s interests and needs at the heart of government.
“We are going to make the most of the opportunities that our departure presents to Northern Ireland - getting out into the world and doing business right across the globe, while at home building a UK that works for everyone.
“As I have said previously, the UK government fully recognises the shared history that exists between the people on the island of Ireland as well as between Ireland and Great Britain so maintaining the common travel area and preserving the Good Friday Agreement are top priorities for us.
“Northern Ireland is the only part of the UK to share a land border with an EU member state, and we recognise the flow of traffic across the border on a daily basis for people going about their daily business is essential as we move forward. There must be no physical infrastructure at the border.”
He added, “I believe that specific solutions can be found to Northern Ireland's unique circumstances, and the UK government will do all in its power to secure an outcome that works for all parts of the UK. I will be reinforcing this message during my discussions.”