The research, conducted by Isme, the Irish Small and Medium Enterprises Association, finds that one in six such companies expect some reduction in staff numbers as a result of Britain leaving the EU.
Isme got replies from 1,416 of its members to the survey, carried out in the second week of March.
It said 68% of the replies came from the services sector; 9% from distribution; 4% from retail; 16% from manufacturing; and 3% from construction.
The survey posed six questions focusing on staffing, turnover, profitability, imports, exports, and relocation post-Brexit.
While many companies appear to feel that Brexit will have little impact on their operations, it is clear that a number are facing a difficult trading environment when Britain leaves the EU.
Just under half (42%) admitted they expect a fall in their turnover, while only 11% said Brexit could lead to an increase.
In turn, 48% of the respondents said they expect their profitability to fall by anywhere up to 20%.
Furthermore, 17% of the companies said Brexit will lead to some reduction in staffing numbers, with 7% saying that the fall could be more than 10%.
A quarter of the companies who replied said more than 20% of their imports or purchases were sterling denominated or from Britain, and 11% said they are considering relocating a part of their business to Britain as a result of Brexit.
Isme said that while the survey indicates Brexit will not impact most of its members, the results come with a health warning.
It said: “They may not represent the broader sectoral impact of Brexit on the SME sector. Isme membership is over-represented in the services sector, by comparison with the CSO breakdown of the 238,000 enterprises in the Irish economy. “
Isme chief executive Neil McDonnell said: “We believe that the services, financial, and insurance sectors on aggregate will have a lower level of direct exposure to Brexit-related impacts than will the industrial, construction, and distribution sectors.
“This does not negate the Brexit-related uncertainties and challenges SMEs face across the country, particularly those in border counties. Services businesses in border counties may be more badly affected by Brexit than other businesses.”