A new report from the Centre for Cities and the Centre for Economic Performance at the London School of Economics, said all cities would see a fall in output due to increasing trade costs.
Aberdeen and Edinburgh were both ranked among the ten most affected cities.
However the study said both cities are also among the best-placed to respond to any predicted economic turbulence.
The study excludes Belfast as the authors said data for Northern Ireland was not available.
The UK government said it was committed to securing a "bold and ambitious" free trade deal and building on the diverse strengths of all the UK's cities and regions.
Meanwhile, Scottish and Welsh government ministers have met in Cardiff to discuss Brexit legislation.
Earlier in July, business advisers PwC said uncertainty about Brexit was having a negative impact on the Scottish economy and housing market.
The London-based Centre for Cities think-tank said all UK cities faced "significant economic challenges" as the UK leaves the EU due to a predicted increase in trading costs.
They produced predicted reductions in economic output for each of the country's cities, for both the scenario of a so-called "soft" Brexit - with the UK joining a free trade area such as the European Free Trade Area (EFTA) - or a "hard" Brexit, where the UK does not come to an immediate deal with the EU and defaults to World Trade Organisation (WTO) rules.
The researchers said either scenario would result in an increase in non-tariff barriers, such as customs checks, border controls, differences in product market regulations and legal hurdles, all increasing the cost of trade.
Under both models, the group predicted that local trade flows and employment shares meant Aberdeen would see the largest reduction in output, measured by gross value added, over the next ten years - of 3.7% under the "hard" Brexit scenario, or of 2.1% under a "soft" Brexit.
Edinburgh was ranked sixth in the table in both models, with reductions of 2.7% and 1.4% respectively. Other cities which feature on the tables include London, Reading, Leeds and Swindon.
However, the researchers said the factors which made the cities likely to suffer in the short term also made them well-placed to respond.
They said the cities were "home to large, highly-skilled labour markets, significant numbers of innovative firms and strong business networks - all of which are crucial in enabling a city to reinvent or adapt its industrial structure to changing economic circumstances".
Prof Stephen Machin from the Centre for Economic Performance said: "The fact that the industrial specialisation and the skill and knowledge intensity of different places are key to local impact should be of significant importance to the design and implementation of policy, especially in the arenas of industrial, skills and labour market strategies."
A UK government spokesman said: "We are committed to a bold and ambitious free trade agreement that works for the whole of the UK.
"The government is engaging extensively with businesses and organisations across the country, and will continue this work throughout the exit process.
"Through the government's modern industrial strategy we will look to build on the diverse strengths of all of the UK's cities and regions."
Scottish Lib Dem leader Willie Rennie contended that Brexit would have a "significant negative impact" regardless of the deal secured, saying the government "cannot just wave these numbers away".
He said: "People last year did not vote to make themselves poorer. The question on the ballot paper was not whether we wanted to destroy our economy and the prosperity of our cities. Giving the people a chance to exit from Brexit with a vote on the deal is the right and democratic thing to do."
Scottish Labour said the report showed the importance protecting jobs and the economy as part of the Brexit deal.
Shadow Scottish Secretary Lesley Laird said: "There should be a jobs-first Brexit, to ensure that our cities such as Aberdeen and Edinburgh can continue to grow. Jobs, the economy and retaining the benefits of the single market and the customs union are our top priority."
Meanwhile, Scottish and Welsh ministers have met in Cardiff to discuss the EU Withdrawal Bill, the legislation planned by the UK government to begin extricating the country from Europe's legal framework.
Scottish Brexit minister Mike Russell and Lord Advocate James Wolffe sat down with Welsh Finance Secretary Mark Drakeford and Welsh government's top lawyer, Counsel General Mick Antoniw.
The devolved administrations fear the legislation could see them lose powers over areas such as fishing and agriculture. The UK government denies this, and says the legislatures will actually gain powers as a result of Brexit.
Aberdeen could be the city worst hit by falling economic output due to a "hard" Brexit, experts have predicted.