Ministers must be cautious over any immediate move to raise salary thresholds for skilled workers from outside the EU, migration advisers say.
Firms warned making it harder for migrants to take up jobs in the UK could force them to expand overseas, a report found.
The business and health departments also raised concerns about potential measures.
The Migration Advisory Committee (MAC) was asked by David Cameron to investigate possible changes to Tier 2 visa requirements for employees from outside the European Economic Area.
The Prime Minister previously said it was "frankly too easy" for some businesses to bring in workers from overseas.
MAC chairman Professor Sir David Metcalf said: "We urge the government to be cautious in making any significant changes to the salary thresholds at this stage because they should not be considered in isolation."
Under the current system migrant workers must be employed in a job with a minimum annual salary of £20,800, while there are also higher thresholds specific to the individual roles.
In its report the MAC analysed a number of possible measures.
It said that raising the salary threshold for occupation-specific roles from the 25th percentile to the median would lock out more than 16,000 workers if firms did not raise wages to meet the level.
This approach would have a "really quite substantial impact", Sir David said.
Nurses and secondary teachers would be among the most "strongly affected" occupations, he added.
The report also said there is "little doubt" that raising the minimum salary threshold to between £31,000 and £39,000 would be "strongly opposed" by many employers and would cause "serious problems" sectors including health and education.
However, the MAC did conclude that there is a good case for increasing the overall minimum threshold from £20,800 as this was based on out-dated calculations.
Firms were questioned by researchers for the study and a number said that increasing thresholds would impact their ability to recruit graduates.
"Overall, a number of firms said that increases in thresholds could lead to increases in the cost of their services, prevent expansion of business and thus possibly cause certain business areas to grow elsewhere in the world at the expense of the UK," the report said.
In another significant finding,the MAC said its provisional conclusion was that there was little evidence to suggest any widespread undercutting of British workers' salaries under the current Tier 2 thresholds.
Sir David also made clear that he was "attracted" to the idea of a skills levy in which firms may have to make a payment for using a migrant.
The MAC will publish a wider review at the end of the year.