The prime minister will be "engaging and listening" to people right across the nation ahead of the divorce talks, according to Number 10.
May will be accompanied by Brexit Secretary David Davis and Welsh Secretary Alun Cairns as Swansea signs a city deal, which is expected to create more than 9,000 jobs and trigger almost £1.3bn in investment.
"I want every part of the UK to be able to make the most of the opportunities ahead and for Welsh businesses to benefit from the freest possible trade as part of a global trading nation," May said.
"Wales' universities already have an excellent international reputation, attracting overseas students and pioneering in research projects here and abroad.
"I also want Wales to be at the forefront of science and innovation – as demonstrated by today's landmark City deal for Swansea.
"The deal is a great example of what can be achieved when the UK Government, the Welsh Government and local authorities work together to secure a deal that benefits the city and the whole of Wales.
"This Government's Plan for Britain will seek to deliver a stronger, fairer United Kingdom and a better deal for ordinary working people in Wales and across the nation."
Davis, May and Cairns will also meet with Labour's First Minister Carwyn Jones as well as representatives from a range of sectors and businesses.
The visit comes just as week after Nicola Sturgeon called for a second Scottish independence referendum between Autumn 2018 and Spring 2019. The proposal will be voted on in Holyrood this week, but May has vowed to block the plebiscite before the UK split from the EU in 2019.
Right now, we should be working together, not pulling apart. We should be working together to get that right deal for Scotland, that right deal for the UK. And so, for that reason, I say to the SNP now is not the time," she told ITV.