The BBC is reporting that after surveying 1000 of its members, the Institute of Directors (IoD) has found that a quarter planned to freeze recruitment and five percent would be planning to cut jobs.
This follows almost two-thirds of companies saying the vote was negative for their business.
Simon Walker, director general of the Institute of Directors, told the BBC's Today Programme: "Business leaders are very, very concerned. Nearly half of them expect the other member states to punish Britain."
Mr Walker said he did not think those that voted for Brexit realised they were voting "for constitutional and economic chaos", but he added half his members did think they could keep going.
James Walsh, head of security practice at Harvey Nash, told SCMagazineUK.com: “I think organisations may pause for thought post-Brexit, but the underlying need for resource and for a job to be done remains, so from a cyber-security recruitment angle I would fundamentally disagree.
“It is now a regular topic of concern at the board level and rightly so, with this the market has and is seeing greater expenditure. Cyber Risk and vulnerability must be addressed whether In of Out of Europe, a company's IP still has the same value today as it did pre Brexit vote.”