Companies cited losing access to talent and funding as major risks when Britain leaves the bloc.
A survey by industry group Ukie polled 75 of the more than 2,000 games firms in the UK, most of which worked in development.
The government said it hoped to "continue to attract" global talent.
A Department for Culture, Media and Sport spokesperson said:  "The UK's creative industries are one of our biggest success stories, and we want to make sure the UK remains a world leader in video games production.
"As the prime minister made clear, we will continue to attract the brightest and best global talent. And we will continue to work with our creative industries to help seize the exciting opportunities that will flow from a new place for Britain in the world."
It is currently conducting a review of the creative industries.
Ukie said this week it wanted to work with the government to "shape a favourable post-EU landscape for our world-leading games and interactive entertainment businesses".
Sales of UK games hit Â£2.96bn last year - more than from either video or music.
Ukie carried out extensive consultations between September and February and found the main concern about Brexit for companies was losing access to skilled workers, with more than 57% saying they employed staff from the European Union.
Some 98% of respondents said EU nationals with the right skills should have a "blanket right" to both live and work in the UK in the future.
"In very competitive, innovative global industries, like games, if UK businesses cannot attract the diverse talent they want and need, some firms are likely to relocate, taking jobs and economic opportunities with them," Ukie said.
Others said divergences with EU laws around data could also pose a risk after Brexit.
A total of 63% said the cost of separating the data they hold on UK customers could impose "significant costs", with one firm saying it may stop publishing games in the UK as a result.
There were also concerns that Brexit could leave UK companies unable to access funding from EU programmes such as Creative Europe - although Ukie said Brexit also offered an opportunity to improve public subsidies for the industry.
More than 60% of games companies forecast growth in their businesses this year, down from 80% in 2016.
Some 40% of British gaming companies say they are considering relocating some or all of their business because of Brexit.