Interest in moving to cities such as Dublin and Berlin has increased over the past few days, said jobs site Indeed.
The top searches were for jobs in marketing, engineering, transport, human resources and retail.
Spokesman Mariano Mamertino said: "Last week, the majority of British citizens voted to exit the European Union, but quickly thereafter many UK-based job seekers started a vote of their own - they jumped online to look for work elsewhere.
"We saw the share of job seekers looking for opportunities outside the UK in European countries doubling in the 48 hours that followed the announcement of a Brexit.
"Most job seekers looked to the very countries of the European Union that Britain will be leaving, with Ireland attracting the most searches.
"This could be early signs of British job seekers' collective vote of no confidence."