Research by the Chartered Institute of Personnel and Development (CIPD) also revealed concerns over employers' investment plans.
A survey of more than 1,000 human resources managers found that just 6% favoured a "hard Brexit."
Employers expect pay settlements to be around 1.1% for the year ahead against a backdrop of anticipated higher inflation, leading to a fall in real wages, said the report.
Gerwyn Davies, of the CIPD, said: "The report points to the UK economy beginning to face some likely headwinds following the UK's decision to leave the European Union.
"The impact of potential restrictions to migrant labour will certainly be exacerbated by the fall we're seeing in business investment intentions.
"It seems that few UK employers want or are ready for a hard Brexit outcome, which all the latest political commentary seems to be pointing towards."
Employers surveyed said it would be harder to recruit and retain European Union migrant workers even before the UK officially leaves the EU.
Of the two thirds of employers employing migrant workers, almost a quarter said they have evidence that EU migrants are already considering leaving the UK in the next 12 months as a result of the referendum result.
John L Marshall, chief executive of the Adecco Group, which helped with the report, added: "For years, the UK has been one of the most attractive countries for EU workers, benefiting from easy access to a large, European talent pool.
"However, the Brexit vote is now seeing UK employers look increasingly concerned about their access to the single market."
Liberal Democrat Treasury spokeswoman Baroness Kramer said: "The CIPD report underscores that Brexit will be a blow to wages at a time when prices are likely to be rising sharply as a consequence of leaving the EU.
"The Government must commit to keeping the UK economy in the single market rather than let its taste for hard Brexit damage ordinary working people and the businesses which sustain our economy.
"These warnings strengthen the need for the people to have a vote on any final Brexit deal."
A Government spokesman said: "The British economy is fundamentally strong and that is why earnings have grown over the past year, and the economy will continue to be strong as we negotiate our departure from the EU."