Speaking to Sky News at the World Economic Forum in Davos, Paul Drechsler said it was crucial that the sense among millions of ordinary workers that they were "not getting a Fair Slice of the pie" was addressed by those at the top of British business in 2017.
"We know how important it is that everyone across the UK feels the value that businesses up and down the country create for individuals, families and communities," he said.
"Pay is part of this, so the CBI has worked with a huge range of members to discuss the best approach to this issue.
"Over 50 million people voted for Trump partly because they felt they were getting a raw deal, and 52% of UK voters supported Brexit at least in part for the same reason - that they are not getting a fair slice of the pie.
"Against that background, it is increasingly important that companies are seen to be acting in a responsible and responsive way to that emerging mood.
"Any company which ignores or goes beyond that runs the risk of damaging the wider reputation of business."
Mr Drechsler's comments mark a rare intervention by the UK's biggest employers' group on the issue of executive pay, underlining the subject's sensitivity ahead of another potentially volatile year for relations between Westminster, the City and major companies.
A series of shareholder revolts at companies including BP, Anglo American and Shire last year sparked outrage in Westminster, prompting Theresa May to pledge a crackdown on corporate excess.
A green paper published towards the end of last year outlined options including the publication of figures showing the gap between the pay of top executives and average workers.
MPs have also launched a separate inquiry covering pay and wider corporate governance issues, with recommendations expected to be unveiled next month.
Mr Drechsler said that most remuneration committees at large companies had done their jobs effectively, but added that "a small number of notable exceptions ... have caused damage to the reputation of business through excessive pay deals".
"At a time when the Prime Minister is attempting to tackle this issue, the decisions that companies reach on boardroom need to be widely understood," he said.
The CBI president added that recent pressure from major institutional investors including Blackrock, Hermes Investment Management and Legal & General Investment Management had helped to "build momentum".
"I can't think of a single time in the past 10 or 20 years when remuneration decisions were expected to be so heavily scrutinised.
"Anything that cannot be clearly justified is especially likely to be challenged," he warned.